Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-3 More Multiplication Properties of Exponents - Practice and Problem-Solving Exercises - Page 437: 45


$(x^{\frac{6}{7}})^{7} = x^{6}$

Work Step by Step

When we raise a power to a power, we multiply the powers together and keep the base. If the bases of two exponential terms are the same, then the exponents are equal to one another. In this exercise, we can set up an equation to set the exponents equal to one another to solve for $x$: $7x = 6$ Divide each side by $7$ to solve: $x = \frac{6}{7}$ Let's rewrite the equation: $(x^{\frac{6}{7}})^{7} = x^{6}$
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