# Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set - Page 522: 50

$\dfrac{1}{4}$

#### Work Step by Step

RECALL: (i) $a^{-\frac{m}{n}}=\dfrac{1}{a^{\frac{m}{n}}}$ (ii) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$ Use the rules above to obtain: $=\dfrac{1}{(-8)^{\frac{2}{3}}} \\=\dfrac{1}{\sqrt[3]{(-8)^2}} \\=\dfrac{1}{\sqrt[3]{64}} \\=\dfrac{1}{\sqrt[3]{4^3}} \\=\dfrac{1}{4}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.