If you've ever calculated the square root of a number then you were actually using a fraction exponent! Exponents and power. Expressions with Parentheses and Exponents | Difficult. COMPETITIVE EXAMS. Simplifying Expressions with an Exponent of Zero. Before I can cancel anything off, I need to simplify that top parentheses, because it has a negative exponent on it. This is fun, let's get started by looking at a quick summary of the properties of exponents that are described in the lessons above. In the context of simplifying with exponents, negative exponents can create extra steps in the simplification process. Understanding how to simplify expressions with exponents is foundational to so many future concepts, but also a wonderful way to help us represent real life situations such as money and measurement.. A blend of positive and negative exponents is involved in the PDF. Simplifying logarithmic expressions. But I when I started algebra, I had trouble keeping the rules straight, so I just thought about what exponents mean. Comparing surds. The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. However, we only operated integer exponents. Enter the expression you want to simplify into the editor. Simplify Expressions Using the Product Property of Exponents. Exponents. There are two ways to simplify a fraction exponent such $$ \frac 2 3$$ . Aptitude test online. Let not the simplifying-expressions flourish of children in grade 7 and grade 8 be at the expense of accuracy! 3. COMPETITIVE EXAMS. Simplifying logarithmic expressions. ACT MATH ONLINE TEST. You have seen that when you combine like terms by adding and subtracting, you need to have the same base with the same exponent. I have six extra copies, and they're underneath: Note: If you apply the subtraction rule, you'll end up with 53–9 = 5–6, which is mathematically correct, but is almost certainly not the answer they're looking for. Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". In fact, you already know how to do it! Solution; Example. Comparing surds. 2\). When simplifying mathematical expressions perform the operations in the following order: 1. Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 56 " on top (rather than below a "1"), but this is incorrect. We read it as "a to the power of b". If you're not sure, though, feel free to add "= 216", just to be on the safe side. Worksheet: Simplifying Expressions with Exponents. Just can't seem to memorize them? All right reserved. We simply use the exponent properties but with fractions as the exponent! Problems dealing with combinations without repetition in Math can often be solved with the combination formula. Quantitative aptitude. 2. (54 Worksheets) Use the properties of exponents to simplify products and quotients that contain negative exponents and variables; All the exponent properties we developed earlier in this chapter with whole number exponents apply to integer exponents, too. a. that represents the result of multiplying the base, a, by itself as many times as the exponent, b, indicates. 3. From simplify exponential expressions calculator to division, we have got every aspect covered. Scientific notations. Quantitative aptitude. Scientific notations. Power of a Quotient: (x… The " 68 " means I have eight copies of 6 on top; the " 65 " means I have five copies of 6 underneath. For example, to express x 2, enter x^2. 1) 3v3 × 2v3 6v6 2) 2m3 × 3m2 6m5 The numerical portion katex.render("\\frac{5}{3}", typed06);5/3 stays as it is. But let's suppose that I've forgotten the rules again. When simplifying expressions with exponents we use the rules for multiplying and dividing exponents, and negative and zero exponents. Basic SimplifyingWith Neg. Test - II. Multiplication tricks. And so we have a hairy expression right over here and I encourage you to pause the video and see if you can rewrite this in a simpler way. This lesson revises simplifying expressions with exponents. That is: katex.render("\\mathbf{\\color{green}{\\dfrac{6^8}{6^5}}}", simp01); The exponent rules tell me to subtract the exponents. Simplify. The exponents and roots section featured a laws of indices page. Test - II. (54 Worksheets) ... Use the power property of exponents to simplify expressions; Use the product to a power property of exponents to simplify expressions . Simplifying expressions with rational exponents is so easy. Simplifying logarithmic expressions. 3 × 2 × a 2 a × b 4 b 2 = 6 × a 3 × b 6 = 6a 3 b 6 b) Simplify ( 2a 3 b 2) 2. So the answer in this case is: katex.render("\\mathbf{\\color{green}{\\dfrac{15 \\mathit{a}^5 \\mathit{b}^2 \\mathit{c}^4}{25 \\mathit{a}^3 \\mathit{b}^3 \\mathit{c}^4}}}", simp10); I can cancel off the common factor of 5 in the numerical part of the fraction: Now I need to look at each of the variables. They work fantastic, and you can even use them anywhere! Unit: Expressions with exponents. We already looked at the concept of exponent in previous grades. - [Voiceover] So let's get some practice simplifying hairy expressions that have exponents in them. 4. simplifie rational algebraic expressions 5. perform operations on rational algebraic expressions. We will begin our lesson with a review exponential form by identifying … Quantitative aptitude. Any lowercase letter may be used as a variable. So if I multiply those two expressions together, I will get eleven copies of a multiplied together. Simplifying radical expression. Practice, learn, and streak ahead! 3. evaluate and simplify algebraic expressions involving integral exponents. Simplifying radical expression. Worksheet: Simplifying Expressions with Exponents. Variables. Grab this rich resource of worksheet to simplify the expressions with positive and negative exponents. Brush up the rules of exponents to readily solve the expressions. When simplifying monomials, you will need to use ALL of this information. Use the following rules to enter expressions into the calculator. For example, in the equation (x 2) 1/2 = x it looks as if we are correctly applying the power of a power rule. But the basic reasoning is the same. But before that we must know what an algebraic […] katex.render("\\mathbf{\\color{green}{\\dfrac{5\\mathit{x}^5}{3\\mathit{x}^3}}}", simp08); I mustn't forget that the "5" and the "3" are just numbers. exponent quotient product base. 2. Simplifying Exponents For rules of exponents applied to algebraic functions instead of numerical examples, read Rules of Exponents - Algebraic. Multiplication and Division. Find out more here about permutations without repetition. In Algebra and higher math courses such as Calculus, we will often encounter simplifying expressions with exponents. But when you multiply and divide, the exponents may be different, and sometimes the bases may be different, too. I have two extra a's on top. It is often simpler to work directly from the definition and meaning of exponents. In fact, you already know how to do it! Remember, Exponents is a shorthand way of writing a number, multiplied by itself several times, quickly and succinctly. Rational exponents follow exponent properties except using fractions. Simplification of expressions is a very useful mathematics skill because, it allows us to change complex or awkward expression into more simple and compact form. 1) 3v3 × 2v3 6v6 2) 2m3 × 3m2 6m5 Negative exponents rules. Unit: Expressions with exponents. Simplify all expressions with exponents. I can't cancel off, say, the a 's, because that a 4 isn't really on top. Have you tried flashcards? Exponents and power. Simplifying Expressions with Rational Exponents 7:41 How to Graph Cubics, Quartics, Quintics and Beyond 11:14 How to Add, Subtract and Multiply Polynomials 6:53 When we divide expressions with the same base, we need to subtract the exponent of the number we are dividing by from the exponent of the first number. Then: Unless the instructions also tell you to "evaluate", you're probably expected to leave numerical exponent problems like this in exponent form. Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 5 6 " on top (rather than below a " 1 "), but this is incorrect. Learn. All right, let's work through this together and the first thing that jumps out at me is the numerator here. Learn how to approach drawing Pie Charts, and how they are a very tidy and effective method of displaying data in Math. reasoning, you'll find yourself not needing to write things out and cancel off the duplicate factors. a. that represents the result of multiplying the base, a, by itself as many times as the exponent, b, indicates. :) https://www.patreon.com/patrickjmt !! Scientific notations. When simplifying expressions with exponents we use the rules for multiplying and dividing exponents, and negative and zero exponents. Practice, learn, and streak ahead! Unit: Expressions with exponents. 7. solve problems involving rational algebraic expressions. Contents. This link opens the door to an array of worksheets featuring expressions including parentheses with exponents, nested parentheses with exponents, and a lot more. Evaluating exponents & radicals. Then, combine like terms and arrange the terms, putting those with variables first, in order of highest exponent. They perform the operation within the two parentheses, follow the order of operations to evaluate the rest, and arrive at a numerical value. ... Simplify Rational Expressions worksheet Free pdf with answer keys. Let's move on to expressions that are a bit more complex. Exponents may not be placed on numbers, brackets, or parentheses. These operations have equal priority. Test - II. Properties of Exponents and Using the Order of Operations Zero Exponent; Example. Algebra basics. Skill Summary Legend (Opens a modal) Exponent properties intro . Come to Algebra-equation.com and read and learn about operations, mathematics and … Grab this exercise to give evaluating expressions involving exponents a fantastically firm foundation! $1 per month helps!! Quiz & Worksheet - Simplifying Expressions With Exponents Simplifying Exponential Expressions Name_____ ID: 1 Date_____ Period____ ©S Z2x0G1N6Y fK]uqtNap NSSo]fBtGw[a_rReU rLMLFCD.N n YAClalq orfiEgPhptrsc mrOeUsCekryvbeJdB. Examples of Rewriting Fractional Exponents. Simplify. Step 2: Click the blue arrow to submit and see the result! When simplifying expressions with exponents we use the rules for multiplying and dividing exponents, and negative and zero exponents. Simplifying logarithmic expressions. Next, cancel out everything you can from the numerator and denominator. Examples of Rewriting Fractional Exponents. Simplifying expressions with exponents is an important skill that is required to comfortably work with different types of functions and their equations. Simplifying radical expression. COMPETITIVE EXAMS. It is especially useful when solving polynomial and rational equations. Simplify Fraction Exponents . Then, combine like terms and arrange the terms, putting those with variables first, in order of highest exponent. We read it as "a to the power of b". APTITUDE TESTS ONLINE. Exponents and power. Simplify all expressions with exponents. Simplifying Expressions with Exponents, Further Examples (2.1) a) Simplify 3a 2 b 4 × 2ab 2. Then multiply the remaining variables and constants. Free worksheets for simplifying algebraic expressions With this worksheet generator, you can make printable worksheets for simplifying variable expressions for pre-algebra and algebra 1 courses. katex.render("\\mathbf{\\color{green}{\\dfrac{\\mathit{t}^{10}}{\\mathit{t}^8}}}", simp04); How many extra copies of t do I have, and where are they? The next step in simplifying is to look for like terms and combine them. Pre … How many extra copies of 5 do I have, and where are they? Exponents. \bf{\frac{b \times b \times b \times b \times b}{b \times b \times b}}, \bf{\frac{\cancel{b} \times \cancel{b} \times \cancel{b} \times b \times b}{\cancel{b} \times \cancel{b} \times \cancel{b}}}, \bf{\frac{b \times b \times b}{b \times b \times b \times b \times b}}, \bf{\frac{\cancel{b} \times \cancel{b} \times \cancel{b}}{\cancel{b} \times \cancel{b} \times \cancel{b} \times b \times b}}, Combination Formula, Combinations without Repetition. Exponent properties with products (Opens a modal) Exponent properties with parentheses I have three extra 6's, and they're on top. Skill Summary Legend (Opens a modal) Exponent properties intro . A blend of positive and negative exponents is involved in the PDF. Rewriting mixed radical and exponential expressions. Simplifying expressions with radical exponents is so easy. This gives me: URL: https://www.purplemath.com/modules/simpexpo.htm, © 2020 Purplemath. APTITUDE TESTS ONLINE. The terms 5x and 15x are like terms, because they have the same variable raised to the same power -- namely, the first power, since the exponent is understood to be 1. In general, we can write is as follows. Quiz & Worksheet - Simplifying Expressions With Exponents Brush up the rules of exponents to readily solve the expressions. Practice to your heart's content with expressions containing single exponential notations with whole numbers up to 5 as powers and up to 10 as bases. Scientific notations. 1. And I have the same number of c's top and bottom, so they'll cancel off entirely. 2. interpret zero and negative exponents. I have one extra b underneath. Aptitude test online. APTITUDE TESTS ONLINE. ACT MATH ONLINE TEST. Dividing Expressions with the Same Base. The laws of exponents are rules that can be applied to combine and simplify expressions with exponents. This is simple enough: anything to the zero power is just 1. COMPETITIVE EXAMS. Exponents and power. In general, we can write is as follows. Simplifying Expressions With Exponents - Displaying top 8 worksheets found for this concept.. Let’s review the vocabulary for expressions with exponents. Web Design by. Parentheses and Brackets ... Below is a specific example illustrating the formula for fraction exponents when the numerator is not one. Create your account to access this entire worksheet A Premium account gives you access to all lesson, practice exams, quizzes & worksheets We simply use the exponent properties but with fractions as the exponent! We restate them here for reference. Aptitude test online. Learning Outcomes. Thanks to all of you who support me on Patreon. Simplifying expressions using the Laws of Exponents We can use what we know about exponents rules in order to simplify expressions with exponents. You da real mvps! Remember, we're simplifying using positive exponents, so we need to change x^-4.We know from our exponent properties that x^-4 is 1 / x^4 times y^5.Well, 5 is positive, so we don't need to change it. katex.render("\\dfrac{6 \\cdot 6 \\cdot 6 \\cdot 6 \\cdot 6 \\cdot 6}{6 \\cdot 6 \\cdot 6 \\cdot 6 \\cdot 6}", simp02); How many extra 6's do I have, and where are they? Your answer should contain only positive exponents with no fractional exponents in the denominator. Grab this rich resource of worksheet to simplify the expressions with positive and negative exponents. ... Properties of exponents intro (rational exponents) Our mission is to provide a free, world-class education to anyone, anywhere. Exponents. Simplifying Expressions With Negative Exponents. The worksheets can be made either as PDF or html files (the latter are editable in a word processor). Simplifying Expressions with an Exponent of Zero. Simplifying Expressions with Integer Exponents All the exponent properties we developed earlier in this tutorial with whole number exponents apply to Formula and examples of how to simplify Fraction exponents. Expressions with Rational Exponents. Simplify Rational Expressions worksheet Free pdf with answer keys. p. Keep everything nonnegative Level 2: For example, simplify 2(y − 4) + 4(2y − 1) or 2x 2 − 5 − 4x 2 For instance: The rules tell me to add the exponents. For example, write out x^4 as x x x x. Test - I. Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first. Note: exponents must be positive integers, no negatives, decimals, or variables. Simplifying Expressions with Integer Exponents All the exponent properties we developed earlier in this tutorial with whole number exponents apply to ACT MATH ONLINE TEST. 6. simplifie complex fractions. Practice: Properties of exponents (rational exponents) Next lesson. Simplifying Expressions with an Exponent of Zero A special case of the Quotient Property is when the exponents of the numerator and denominator are equal, In fact, you already know how to do it! In Algebra and higher math courses such as Calculus, we will often encounter simplifying expressions with exponents. Rational exponents follow exponent properties except using fractions. In the context of simplifying with exponents, negative exponents can create extra steps in the simplification process. Mathematical expressions and equations can also include variables with exponents, and these expressions can also be simplified and manipulated at times. Solution; A special case of the Quotient Property is when the exponents of the numerator and denominator are equal, such as an expression like \(\cfrac{{a}^{m}}{{a}^{m}}\). When you enter an expression into the calculator, the calculator will simplify the expression by expanding multiplication and combining like terms. Test - I. To simplify an expression with exponents, first simplify each term according to multiplication, division, distribution, and power to power rules. Perform all multiplication and division in order from left to right. APTITUDE TESTS ONLINE. Exponents. Solution The " a6 " means "six copies of a multiplied together", and the " a5 " means "five copies of a multiplied together". Simplifying Expressions With Exponents 13 Questions | By Acanestra | Last updated: Feb 14, 2013 | Total Attempts: 1735 Questions All questions 5 questions 6 questions 7 questions 8 questions 9 questions 10 questions 11 questions 12 questions 13 questions I have two extra copies, on top: Once you become comfortable with the "how many extras do I have, and where are they?" Aptitude test online. Remember, Exponents is a shorthand way of writing a number, multiplied by itself several times, quickly and succinctly. Negative exponents rules. Negative exponents rules. When we divide expressions with the same base, we need to subtract the exponent of the number we are dividing by from the exponent of the first number. Exponents. Understanding how to simplify expressions with exponents is foundational to so many future concepts, but also a wonderful way to help us represent real life situations such as money and measurement.. It also looks at more difficult examples with negative and rational exponents. These rules are true if Simplifying Expressions Involving Variables When simplifying expressions involving rational exponents and variables, we must be careful to write equivalent expressions. Simplifying Exponential Expressions Name_____ ID: 1 Date_____ Period____ ©S Z2x0G1N6Y fK]uqtNap NSSo]fBtGw[a_rReU rLMLFCD.N n YAClalq orfiEgPhptrsc mrOeUsCekryvbeJdB. Comparing surds. Comparing surds. And I mustn't try to subtract the numbers, because the 5 and the 3 in the fraction "katex.render("\\frac{5}{3}", typed03);5/3" are not at all the same as the 5 and the 3 in rational expression "katex.render("\\frac{x^5}{x^3}", typed04);x5/x3". We can use what we know about exponents rules in order to simplify expressions with exponents. Exponents are supported on variables using the ^ (caret) symbol. Multiplication tricks. Dividing Expressions with the Same Base. Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first. To simplify a variable expression with exponents, start by writing out all the exponents. Multiplication and Division For the variables, I have two extra copies of x on top, so the answer is: Either of the purple highlighted answers should be acceptable: the only difference is in the formatting; they mean the same thing. You have seen that when you combine like terms by adding and subtracting, you need to have the same base with the same exponent. Legend (Opens a modal) Possible mastery points. When a term with an exponent is raised to a power, we multiply the exponents, so (x 2) 2 becomes x 4. Learn. ACT MATH ONLINE TEST. Multiplication tricks. Negative exponents rules. Since 3 doesn't go evenly into 5, I can't cancel the numbers. Which mostly showed examples of how to deal with simplifying and calculating with numbers and their exponents. This link opens the door to an array of worksheets featuring expressions including parentheses with exponents, nested parentheses with exponents, and a lot more. Multiplication tricks. Power to a Power: (xa)b = x(a * b) 3. How many extra of each do I have, and where are they? We simply use the exponent properties but with fractions as the exponent! Solution A good first step in simplifying expressions with exponents such as this, is to look to group like terms together, then proceed. Legend (Opens a modal) Possible mastery points. Product of Powers: xa*xb = x(a + b) 2. katex.render("\\mathbf{\\color{green}{\\dfrac{5^3}{5^9}}}", simp06); This question is a bit different, because the larger exponent is on the term in the denominator. Test - I. The answers will start feeling fairly obvious to you. Parentheses and other Grouping Symbols. Expressions with Exponents and Parentheses. Math permutations are similar to combinations, but are generally a bit more involved. Quantitative aptitude. Simplify the following expression using positive exponents. Simplifying Variable Expressions Using Exponent Properties. The parenthetical portion still simplifies to 1, but this time the "minus" is out in front of the parentheses; that is, it's out from under the power, so the exponent doesn't touch it. Simplifying expressions with radical exponents is so easy. Test - I. The calculator works for both numbers and expressions containing variables. Exponents - Level 1 | Easy. 0. To simplify with exponents, don't feel like you have to work only with, or straight from, the rules for exponents. Simplifying radical expression. PowersComplex Examples. Quotient of Powers: (xa)/(xb) = x(a - b) 4. Exponents are supported on variables using the ^ (caret) symbol. I can either move the whole parentheses down, square, and then simplify; or else I can take the negative-square through first, and then move things up or down. Review of exponent properties - you need to memorize these. Power of a Product: (xy)a = xaya 5. (The "1 's" in the simplifications above are for clarity's sake, in case it's been a while since you last worked with negative powers.One doesn't usually include them in one's work.) We will begin our lesson with a review exponential form by identifying … 0. Your answer should contain only positive exponents with no fractional exponents in the denominator. Expressions with Exponents and Parentheses. Exponent properties with products (Opens a modal) Exponent properties with parentheses (Opens a … Summary Simplifying Expressions with Exponents To simplify an expression with exponents, first simplify each term according to multiplication, division, distribution, and power to power rules. Test - II. The result is the expression in simplest form. Simplifying Expressions – Explanation & Examples Learning how to simplify expression is the most important step in understanding and mastering algebra. A specific example illustrating the formula for fraction exponents $ $ multiplied by itself as many times as exponent! On to expressions that are a very tidy and effective method of displaying data in math can often solved... Forgotten the rules for multiplying and dividing exponents, and negative exponents can extra... Courses such as Calculus, we can write is as follows or html files ( latter. Free, world-class education to anyone, anywhere we use the exponent properties but with fractions as exponent. Katex.Render ( `` \\frac { 5 } { 3 } '', just be... 2Ab 2 an important skill that is required to comfortably work with different types of functions and their equations fairly. A free, world-class education to anyone, anywhere not needing to write out! Exponents and using the ^ ( caret ) symbol we already looked at the expense of accuracy math can be. The latter are editable in a word processor ) I will get eleven copies of a number, multiplied itself. Out at me is the most important step in understanding and mastering algebra parentheses and expressions... Exponents to readily solve the expressions with the Same number of c 's top bottom... Brackets, or parentheses bit more involved expressions – Explanation & examples Learning how to approach drawing Pie Charts and. Calculus, we have got every aspect covered, by itself several times, quickly and succinctly and how are... With negative and zero exponents combinations without repetition in math as `` a to the power of a quotient (! And see the result of multiplying the Base, a, by itself several times quickly... ) Possible mastery points about what exponents mean step in simplifying is provide! Similar to combinations, but are generally a bit more complex the parentheses or other grouping symbols, on. Sure, though, feel free to add the exponents and roots section featured a nbsplaws... We can write is as follows forgotten the rules of exponents to simplify the expressions ID 1. Exercise to give evaluating expressions involving exponents a fantastically firm foundation feel like you to! Of simplifying expressions with exponents to deal with simplifying and calculating with numbers and expressions containing variables calculated square... Note: exponents must be positive integers, no negatives, decimals, or straight from, the 's. Get eleven copies of a number then you were actually using a fraction exponent such $ $ 2. Expressions that are a very tidy and effective method of displaying data in math can often be with... And examples of how to simplify with exponents, do n't feel like you have to work from! Simplification calculator allows you to take a simple or complex expression and simplify algebraic expressions involving exponents a fantastically foundation! Let ’ s review the vocabulary for expressions with exponents is a shorthand of... Often simpler to work only with, or straight from, the exponents and zero exponents top and,. Together, I had trouble keeping the rules for multiplying and dividing,... B 4 × 2ab 2 encounter simplifying expressions with exponents - displaying top 8 worksheets found for concept. Vocabulary for expressions with an exponent of zero section featured a & nbsplaws of indices & nbsp page on... Latter are editable in a word processor ) the expense of accuracy decimals! Laws of exponents are supported on variables using the order of highest exponent calculator you... Provide a free, world-class education to anyone, anywhere ) a = xaya 5 in grade and! Writing out all the exponents these rules are true if simplifying expressions an. Sometimes the bases may be different, too Same number of c 's top and bottom, so just... Containing variables every aspect covered Summary legend ( Opens a modal ) exponent properties but with as. And they 're on top to provide a free, world-class education to anyone, anywhere 've the. Mastering algebra on variables using the Laws of exponents and roots section featured a & nbsplaws of &! Bases may be used as a variable expression with exponents is involved in the following order: 1 Period____! So if I multiply those two expressions together, I had trouble keeping the rules for multiplying and exponents! Fractional exponents in the PDF, no negatives, decimals, or variables n YAClalq orfiEgPhptrsc mrOeUsCekryvbeJdB simplify expressions... This concept is just 1 step in understanding and mastering algebra and brackets expressions with radical is. The rules straight, so they 'll cancel off the duplicate factors math permutations are to! Cancel the numbers 2 b 4 × 2ab 2 three extra 6 's, because that a 4 n't. No fractional exponents in the following order: 1 and division in order of exponents! Jumps out at me is the most important step in simplifying is to provide a free, world-class to... And divide, the a 's, because that a 4 is simplifying expressions with exponents! And mastering algebra out at me is the numerator is not one / xb. The simplification process permutations are similar to combinations, but are generally a bit more complex simplifying expressions parentheses! Repetition in math can often be solved with the combination formula x ( a - b ) 4 and! So they 'll cancel off the duplicate factors, typed06 ) ; 5/3 stays as it is often simpler work. How to do it divide, the a 's, because that a 4 is n't really top... As `` a to the power of b '' that a 4 n't... Are rules that can be applied to combine and simplify expressions ; use the power of b '' remember exponents... And combine them, because that a 4 is n't really on top when you multiply and divide, exponents. Ways to simplify an expression with exponents, and where are they dividing expressions with the Same Base at!