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: 42



Work Step by Step

Recall the rational exponent property (pg. 382): $\sqrt[n]{a}=a^{\frac{1}{n}}$ Applying this property, we get: $=7^{\frac{1}{7}}7^{\frac{1}{3}}$ Next, recall the basic exponent property (pg. 360): $a^ma^n=a^{m+n}$ Applying this property to our last equation, we get: $=7^{\frac{1}{7}+\frac{1}{3}}$ $=7^{\frac{3}{21}+\frac{7}{21}}$ $=7^{\frac{3+7}{21}}$ $=7^{\frac{10}{21}}$ Now, recall the rational exponent property (pg. 382): $a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$ We use this property to rewrite the result as a radical: $7^{\frac{10}{21}}=\sqrt[21]{7^{10}}$
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