Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - 6-4 Rational Exponents - Practice and Problem-Solving Exercises - Page 386: 29



Work Step by Step

We are asked to replace radicals with exponents in the given equation: $\sqrt[2]{(7x)^3}$ Recall the rational exponent property (pg. 382): $a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$ Applying this property ($m=3$, $n=2$, $a=7x^3$), we get: $\sqrt{(7x)^3}=\left[(7x)^3\right]^{\frac{1}{2}}=\left(7x\right)^{\frac{3}{2}}$
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