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Simplify: \(\dfrac{y+\dfrac{1}{x}}{\dfrac{x}{y}}\) Solution. Begin by combining the expressions in the numerator into one expression. \[\begin{align*} …. Natural boobs lesbian

Mar 21, 2018 · Answer: years after the population will be doubled. Explanation: According to the question, There is a town which population is increasing per year. And, it will be doubled in years. The steps he could have used instead to simplify the expression (5 Superscript 4 Baseline) cubed Hence, the correct option is A. What is simplification of an expression? Usually, simplification involves proceeding with the pending operations in the expression .To simplify the given expression \((e^\frac{l^n}{2\ln e})\), we can use the property of logarithms that states \(\ln e = 1\). Therefore, the expression simplifies to \(e^\frac{l^n}{2}\). To find out in how many years the population of the town will double, we need to solve the equation where the initial population is multiplied by 2, which ...College Algebra. 1st Edition • ISBN: 9781938168383 (1 more) Jay Abramson, OpenStax. 4,642 solutions. 1 / 4. Find step-by-step College algebra solutions and your answer to the following textbook question: Simplify each power of i.. Example 1.7.1: Simplifying Rational Expressions. Simplify x2 − 9 x2 + 4x + 3. Solution. (x + 3)(x − 3) (x + 3)(x + 1) Factor the numerator and the denominator x − 3 x + 1 Cancel common factor (x + 3) Analysis. We can cancel the common factor because any expression divided by itself is equal to 1. Water is sometimes removed from the products of a reaction by placing the products in a closed container with excess P4O10. Water is absorbed by the following reaction. P4O10 + 6H2O es001-1.jpg 4H3PO4 What is the mole ratio of water to H3PO4? Do not simplify the ratio. Hes001-2.jpgO:Hes001-3.jpgPOes001-4.jpg = :4You may miss out on bank insurance, credit card rewards and the benefits of technology if you oversimplify your finances. By clicking "TRY IT", I agree to receive newsletters and p...Plot points at (0, 3), (0, 1), and (0, 5). What is true about all points with an x-coordinate of 0? A group consisting of 21 aggressive zombies quadruples in size every hour.In today’s digital age, the ability to convert files from one format to another has become increasingly important. One such conversion that is commonly needed is converting JPG ima... If 1 minus x squared is greater than or equal to 3, then x squared must be less than -2. Since x squared cannot be less than a negative number, the function is undefined for all values of x. Study with Quizlet and memorize flashcards containing terms like Given f (x) = x - 2 andmc001-1.jpg which of the following values is not in the domain of ... 1. The Product of powers property: 2. The Power of a power property: In this case, given: You need to follow these steps in order to simplify it: 1. Apply the Product of powers property: 2. Apply the Power of a power property: 3. Finally, since and , you get:A. Solve: 3 ln x = ln 216. B. Identify the solution set of 3 ln 4 = 2 ln x. C 8. Identify the solution set of 6 ln e = eln 2x. B 3. A town predicts that its population will double in es001-1.jpg years. Simplify the expression.Engineering. Computer Science. Computer Science questions and answers. Simplify each of the following powers of i. es^ (001)-1.jpg.Feb 23, 2020 · 7 6 5 00 8 2 1 3 4 3. 456 4. 4 and Decide whether each statement is TRUE or FALSE. If the statement is FALSE, correct the statement. 1. 2. 23 21 and 2 … 2 are vertical angles. 41 and 5 are corresponding angles. 2 and 5 are alternate exterior angles. 6 are alternate interior angles. 5. Final answer: The function g(x) = |x-3| is neither even nor odd. The function g(x) = x + x² is also neither even nor odd. Explanation: To determine whether a function is even, odd, or neither, we need to check if it satisfies the properties mentioned earlier.. For the function g(x) = |x-3|: Substitute -x for x in the function: g(-x) = |(-x)-3| = |-x+3|How much would an order of 1 slice of cheese pizza and 3 sodas cost? A. $3.25 B. $5.25 C. $7.75 D. $7.25. star. 4/5. heart. 47. verified. Verified answer. Which statements are true regarding undefinable terms in geometry? Select two options. A point's location on the coordinate plane is indicated by an ordered pair, (x, y). A point has one ...Simplify. Explain. heart outlined ... Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Jpg degrees. Es004-1. Jpg degrees. heart. 40. verified. Verified answer. Accenture has signed a multi year agreement to help a mobile telecom provider. star. 4/5.Study with Quizlet and memorize flashcards containing terms like Use the formula for radian measure to calculate the measure of a central angle in a circle having a radius of 12 cm and intercepting an arc of 21 cm. es001-1.jpg The angle has a measure of _____ radians., Convert 1 radian to degrees. Round your answer to the nearest degree., …Study with Quizlet and memorize flashcards containing terms like A car battery produces electrical energy with the following chemical reaction. Pb + PbO2 + 2H2SO4 es001-1.jpg; 2PbSO4 + 2H2O What is the mole ratio of PbO2 to water? How many moles of water are produced if 5.43 mol PbO2 are consumed?, The fuel used to power the booster rockets …To simplify an expression with fractions find a common denominator and then combine the numerators. If the numerator and denominator of the resulting fraction are both divisible by the same number, simplify the fraction by dividing both by that number. Simplify any resulting mixed numbers. Show moreSimplify. Explain. heart outlined ... Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1.5. Compare and contrast the absolute value of a real number to that of a complex number. imaginary number complex plane real number negative always positive. We have an expert-written solution to this problem! Study with Quizlet and memorize flashcards containing terms like Simplify each of the following powers of i., √−100, √9 + √−36 ...es001-1.jpg. 920136168 920136168 26.01.2021 Math Secondary School answered Classify the following polynomials. Combine any like terms first. es001-1.jpg See answers Advertisement Advertisement navyabalubaghi ... कंपनी ने जिसका लेखांकन वर्ष कैलेंडर वर्ष है 1 अप्रैल 2013 को ₹30000 की लागत वाली एक मशीन के लिए कि इस नंबर 2013 को ₹20000 ...Create an account to view solutions. 1 / 4. Find step-by-step Precalculus solutions and your answer to the following textbook question: Simplify each power of i to i, 1,-i, or -1. $$ i^2 $$.Es001-1.jpg - 13235712. denishastockdale21 denishastockdale21 26.10.2019 ... Substitute r(x) = 2√x and s(x)= √x and simplify (rs)(x) =2√x . √x (rs)(x) =2x ...Algebra II For Dummies. Performing operations on complex numbers requires multiplying by i and simplifying powers of i. By definition, i = the square root of –1, so i2 = –1. If you want i3, you compute it by writing i3 = i2 x i = –1 x i = – i. Also, i4 = i2 x i2 = (–1) (–1) = 1. And then the values of the powers start repeating ...Indices Commodities Currencies Stocks7 6 5 00 8 2 1 3 4 3. 456 4. 4 and Decide whether each statement is TRUE or FALSE. If the statement is FALSE, correct the statement. 1. 2. 23 21 and 2 … 2 are vertical angles. 41 and 5 are corresponding angles. 2 and 5 are alternate exterior angles. 6 are alternate interior angles. 5.Ammonium hydrogen phosphate ((NH4)2HPO4), a common fertilizer, is made by reacting phosphoric acid (H3PO4) with ammonia according to the following reaction. 2NH3 + H3PO4 es001-1.jpg (NH4)2HPO4 What is the ratio of NH3 to H3PO4? NHes001-2.jpg:Hes001-3.jpgPOes001-4.jpg = 2:The transformed function is translated to the right along the x-axis and stretched by a scale factor of 2.. What is transformation? A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.. Given is a function, y = being transformed into y = . We see, that, in the function, …Dimensional Analysis 1. I have 470 milligrams of table salt, which is the chemical compound NaCl. How many liters of NaCl solution can I make if I want the solution to be 0.90% NaCl? (9 grams of salt per 1000 grams of solution). The density of the NaCl solution is 1.0 g solution/mL solution. All real numbers x, except x = 0. Identify the vertical asymptote of the function. f (x)= x^2 + 1/ 3 (x-8) 8. What are the vertical asymptotes of f (x)= 10/x^2 - 1. 1, -1. Wavelength varies inversely with frequency. Let k be the product of wavelength and frequency. Complete the table using the inverse variation relationship. Check all of the boxes that apply. B. 4,5. If x < 5 and x > c, give a value of c such that there are no solutions to the compound inequality. Explain why there are no solutions. The value of c could be 5 or any number greater than 5. Identify the graph of the inequality 2 (2x - 1) + 7 < 13 or -2x + 5 -10. C.Study with Quizlet and memorize flashcards containing terms like How many terms are in the algebraic expression -7+12x^4-5y^8+x?, What is the simplified expression for 5ab+9ab-ab?, Simonne used the following steps to simplify the given expression. 12-3(-2x+4) Step 1: 12+(3)(-2x)+(-3)(4) Step 2: 12+6x+(-12) Step 3: 12+(-12)+6x Step 4: 0+6x Step 5: 6x …Free Cube Root calculator - Find cube roots of any number step-by-stepStudy with Quizlet and memorize flashcards containing terms like A car battery produces electrical energy with the following chemical reaction. Pb + PbO2 + 2H2SO4 es001-1.jpg; 2PbSO4 + 2H2O What is the mole ratio of PbO2 to water? PbOes001-2.jpg:Hes001-3.jpgO = 1: How many moles of water are produced if 5.43 mol PbO2 are consumed?, The fuel …Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify. Statistics. Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution. Physics. …Answer: years after the population will be doubled. Explanation: According to the question, There is a town which population is increasing per year. And, it will be doubled in years.. Therefore, it will be two times of its initial value after 10/2 years. let after x …A rational expression is an expression of the form p(x) q(x), where p and q are polynomials and q ≠ 0. Remember, division by 0 is undefined. Here are some examples of rational expressions: −1342 7y 8z 5x+2 x2−7 4x2+3x−1 2x−8. Notice that the first rational expression listed above, −1342, is just a fraction. Since a constant is a ...Mar 14, 2018 · Plot points at (0, 3), (0, 1), and (0, 5). What is true about all points with an x-coordinate of 0? A group consisting of 21 aggressive zombies quadruples in size every hour. Step 1: Enter the inequality below which you want to simplify. The inequality calculator simplifies the given inequality. You will get the final answer in inequality form and interval notation. Step 2: Click the blue arrow to submit. Choose "Simplify" from the topic selector and click to see the result in our Algebra Calculator! Examples. SimplifyOne to any power is one. Multiply i i by 1 1. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.Example 1.7.1: Simplifying Rational Expressions. Simplify x2 − 9 x2 + 4x + 3. Solution. (x + 3)(x − 3) (x + 3)(x + 1) Factor the numerator and the denominator x − 3 x + 1 Cancel common factor (x + 3) Analysis. We can cancel the common factor because any expression divided by itself is equal to 1.Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify. Statistics. Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution. Physics. …All real numbers x, except x = 0. Identify the vertical asymptote of the function. f (x)= x^2 + 1/ 3 (x-8) 8. What are the vertical asymptotes of f (x)= 10/x^2 - 1. 1, -1. Wavelength varies inversely with frequency. Let k be the product of wavelength and frequency. Complete the table using the inverse variation relationship.A JPG file is one of the most common compressed image file types and is often created by digital cameras. At times, you may need to convert a JPG image to another type of format. Y...Therefore, the like radical to 3√54 is 3√ (2 * 3²). 1. Start with the given radical: 3√54. 2. Break down 54 into prime factors: 54 = 2 * 3². 3. Rewrite the radical using the prime factorization: 3√ (2 * 3²). 4. The like radical is then 3√ (2 * 3²), as it represents the same value as the original radical, 3√54. Select the expression that is equivalent to: 3 sqrt 1089 Simplify completely: a and 99. Simplify: c and b. Simplify: b and b. Simplify: a and b. Simplify completely. b. 3a + 2 − 6aa2 − 4 = 1a − 2. The students is incorrect. There are no solutions to this equation because first, you would find the LCD which is (a2) (a2). Next, you would simplify making 3 (a2)6aa2. Then, you would expand making 3a6a2. The next step is adding 6 to both sides. Soon, you get 4a/4 which equals 8/4. Simplify inside the parentheses by dividing coefficients, subtracting the exponents on like bases, and raising the resulting expression to the –3 power. Then, write bases with positive exponents. ... Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Jpg …Expert-Verified Answer. question. 40 people found it helpful. MrRoyal. The reference angle is the smallest angle between the terminal side and the x-axis. 300 degrees is in the 4th …Apr 7, 2020 · The steps he could have used instead to simplify the expression (5 Superscript 4 Baseline) cubed Hence, the correct option is A. What is simplification of an expression? Usually, simplification involves proceeding with the pending operations in the expression . Nov 17, 2020 · The Steps to simplifying the 4 + x² - 2 [1 -2x³ + 2x² + 13x - 3 /( x - 3)] are: Step 1: Find the quotient. Step 2: Subtract the result from 1. Step 3: Multiply the result by –2. Step 4: Add the result to 4 + x². What is Algebra? A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. We can apply the properties of fractions to rational expressions, such as simplifying the expressions by canceling common factors from the numerator and the denominator. To do this, we first need to factor both the numerator and denominator. Let’s start with the rational expression shown. x2 + 8x + 16 x2 + 11x + 28 x 2 + 8 x + 16 x 2 + …Es001-1.jpg a = b = c = - 24826521. vinaysingh9383 vinaysingh9383 06.10.2020 Math Secondary School answered ... (Simplifying Products and Quotients of Powers)Simplify each power of i. 1/i^-12. Verified Solution. 3m. Play a video: This video solution was recommended by our tutors as helpful for the problem above. 65.Step 1: Enter an exponential expression below which you want to simplify. The exponent calculator simplifies the given exponential expression using the laws of exponents. Step 2: Click the blue arrow to submit. Choose "Simplify" from the topic selector and click to see the result in our Algebra Calculator! ExamplesStudy with Quizlet and memorize flashcards containing terms like Mason opens a savings account by making a $165.85 deposit. Every week, he deposits another $20.50 in the account. Write an expression that shows the amount of money that will be in the account x weeks after Mason opens it. 165.85x + 20.5 165.85 - 20.5x 165.85 + 20.5 + x 165.85 + … Simplifying Powers of i. Step 1: Rewrite the power of i using the power of a power, and the product properties of exponents to write the expression using terms of i 2 = − 1, and i 4 = ( i 2) 2 ... Algebra II For Dummies. Performing operations on complex numbers requires multiplying by i and simplifying powers of i. By definition, i = the square root of –1, so i2 = –1. If you want i3, you compute it by writing i3 = i2 x i = –1 x i = – i. Also, i4 = i2 x i2 = (–1) (–1) = 1. And then the values of the powers start repeating ...The steps he could have used instead to simplify the expression (5 Superscript 4 Baseline) cubed Hence, the correct option is A. What is simplification of an expression? Usually, simplification involves proceeding with the pending operations in the expression. Simplification usually involves making the expression simple and easy to …1-i. Click the card to flip 👆. Find the sum of i¹² and i⁵⁵. Click the card to flip 👆. 1 / 14.Precalculus. Determine if Odd, Even, or Neither f (x)=x. Step 1. Find . Tap for more steps... Find by substituting for all occurrence of in . Remove parentheses. Step 2.How to solve your equation. To solve your equation using the Equation Solver, type in your equation like x+4=5. The solver will then show you the steps to help you learn how to solve it on your own.5. Compare and contrast the absolute value of a real number to that of a complex number. imaginary number complex plane real number negative always positive. We have an …Jan 4, 2022 · Simplify. Explain. heart outlined ... Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. 7 6 5 00 8 2 1 3 4 3. 456 4. 4 and Decide whether each statement is TRUE or FALSE. If the statement is FALSE, correct the statement. 1. 2. 23 21 and 2 … 2 are vertical angles. 41 and 5 are corresponding angles. 2 and 5 are alternate exterior angles. 6 are alternate interior angles. 5.Further simplifying this equation, we obtain x^2 - 3x - 4 = x^2 - 5x + 6 which can then be solved with algebraic methods. Explanation: To solve the given equation by multiplying each term by the lowest common denominator (LCD), which is 3x(x-2) , we need to eliminate the fractions first.Precalculus. Determine if Odd, Even, or Neither f (x)=x. Step 1. Find . Tap for more steps... Find by substituting for all occurrence of in . Remove parentheses. Step 2.In the context of complex numbers, the imaginary unit ' i ' has a cyclic pattern of powers. Specifically, i^1 is i, i^2 is -1, i^3 is -i, and i^4 is 1. After this, the cycle repeats. …Click here 👆 to get an answer to your question ️ Simplify mc002-1. Jpg –100,000 mc002-2. Jpg mc002-3. Jpg 100,000. See what teachers have to say about Brainly's new learning tools! ... Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Jpg …Video transcript. - So we have the graphs of two functions here. We have the graph y equals f of x and we have the graph y is equal to g of x. And what I wanna do in this …Fraction Addition. Fraction Subtraction. a c + b c = a + b c a c + b c = a + b c. Add the numerators and place the sum over the common denominator. a c − b c = a − b c a c − b c = a − b c. Subtract the numerators and place the difference over the common denominator. To multiply or divide fractions, and LCD is NOT needed.adioabiola. The simplification of i²² is equal to; -1. According to the question; We are required to determine the value of i²². By complex numbers; i = √-1. i² = -1. i³ = -1 × √-1 = -1 × i = -i. i⁴ = i² × i² = -1 × -1 = 1.Simplify. Explain. heart outlined ... Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Jpg degrees. Es004-1. Jpg degrees. heart. 40. verified. Verified answer. Accenture has signed a multi year agreement to help a mobile telecom provider. star. 4/5. Simplifying Powers of i. Step 1: Rewrite the power of i using the power of a power, and the product properties of exponents to write the expression using terms of i 2 = − 1, and i 4 = ( i 2) 2 ... Study with Quizlet and memorize flashcards containing terms like Which graph shows the solution to the equation 4x - 3 = 8?, To solve e4 - 3x = mr001-1.jpgx + 9 by graphing, …Researchers say it's analogous to shouting across a rowdy bar. It’s a real sea of noise in the oceans these days. On top of the normal sounds of singing cetaceans, cracking shrimp,...(1): "s0" was replaced by "s^0". (2): Dot was discarded near "1.j". Step 1 : Final result : es - jpgClick here 👆 to get an answer to your question ️ A town predicts that its population will double in e^(ln 10)/2ln e years. Simplify the expression. In how mIdentify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Jpg degrees.Find more answers. plus. Ask your question. What is the measure of angle 2? es001-1.jpg = - 23560972.Clerk, an early-stage startup, wants to make it easy for front-end web developers to add identity to an application. Developers building front-end Jamstack web applications often s...Find more answers. plus. Ask your question. What is the measure of angle 2? es001-1.jpg = - 23560972.so i^4 is back to 1. Take the power , divide by 4 and look to the chart for the remainder. If the remainder is 0 then i to that power is 1. 1 i. 2 -1. 3 -i. i^22. Take 22/4 = 5 remainder 2. The remainder is 2 so i^22 = -1.May 29, 2020 · Hence, the order of steps needed to simplify this expression is. Step 1. Step4. Step3. Step2. What is the simplification? Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving. Here given expression is. Step 1:-Simplify the parenthesis. Step 2:- Evaluate exponents

Select all of the following that you included in your answer. The answer is not correct. The student did not use the quotient of powers property correctly. The student divided the exponents within the parentheses instead of subtracting. The correct simplified form is x to the two-fifths power. <3 Learn with flashcards, games, and more — for free.. Aznudes gay

simplify es001 1 jpg

A JPG file is one of the most common compressed image file types and is often created by digital cameras. At times, you may need to convert a JPG image to another type of format. Y...Step 1. To simplify this fr... Simplify. Type your answer as a fraction only (example 3/7. Do not put spaces in your answer. 585135 Question 2 Evaluate and simplify. Type your answer as a fraction orly (example: 3/7. Do not put spaces in your answer. 2018 ⋅ 9936 Question 3 The fraction below is undertred. 08 Question 3 The fraction below is ...Complete the steps to solve the equation 4e2 + 2x = x − 3 by graphing. Write a system of equations. y = 4e2 + 2x and y =. Graph the system. Use the graphing calculator to graph each equation. Identify the solutions. The of the points where the graphs of the equations intersect are the solutions to the original equation.Jan 17, 2022 · Simplify. Explain. heart outlined ... Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Select the expression that is equivalent to: 3 sqrt 1089 Simplify completely: a and 99. Simplify: c and b. Simplify: b and b. Simplify: a and b. Simplify completely. b.Es001-1.jpg - 13235712. denishastockdale21 denishastockdale21 26.10.2019 ... Substitute r(x) = 2√x and s(x)= √x and simplify (rs)(x) =2√x . √x (rs)(x) =2x ...Step 1. To simplify this fr... Simplify. Type your answer as a fraction only (example 3/7. Do not put spaces in your answer. 585135 Question 2 Evaluate and simplify. Type your answer as a fraction orly (example: 3/7. Do not put spaces in your answer. 2018 ⋅ 9936 Question 3 The fraction below is undertred. 08 Question 3 The fraction below is ...Right triangle mc001-1.jpg has mc001-2.jpg, a = 6, and b = mc001-3.jpg. Use this information to find mc001-4.jpg. This question hasn't been solved yet!Identify the reference angle es001-1. Jpg for each given angle, es001-2. Jpg. Es001-3. Jpg degrees. Es002-1. Jpg degrees. Es003-1. Jpg degrees. Es004-1. Jpg degrees. heart. 40. verified. Verified answer. Accenture has signed a multi year agreement to help a mobile telecom provider. star. 4/5. heart. 4. verified. Verified answer. Which …A town predicts that its population will double in es001-1. Jpg years. Simplify the expression. In how many years will the popul. ation of the town double?. SAT. Answer Comment. 1 answer: Alexxandr [17] 2 years ago. 8 0. Answer: 5. ... 5 · 1 answer. Tyler is preparing a speech on skateboarding for his physics class. For speech support, he is ... Does this mean that it is not possible to write es002-1.jpg as a single radical? ... Simplify the quotient of the exponential expressions by getting a common ... Example 7.1.3. Determine the domain: x4 + x3 − 2x2 − x x2 − 1. Solution: To find the restrictions to the domain, set the denominator equal to 0 and solve: x2 − 1 = 0 (x + 1)(x − 1) = 0. x + 1 = 0 or x − 1 = 0 x = − 1 x = 1. These two values cause the denominator to be 0. Hence they are restricted from the domain.Select all of the following that you included in your answer. The answer is not correct. The student did not use the quotient of powers property correctly. The student divided the exponents within the parentheses instead of subtracting. The correct simplified form is x to the two-fifths power. <3 Learn with flashcards, games, and more — for free..

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