# Chapter 7 - Section 7.2 - Rational Exponents - Exercise Set - Page 522: 103

$\sqrt[8]{x}$

#### Work Step by Step

RECALL: (1) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (2) $\sqrt{a} = a^{\frac{1}{2}}$ (3) $(a^m)^n= a^{mn}$ Use rule (2) above to obtain: $=\sqrt[4]{x^{\frac{1}{2}}}$ Use rule (1) above to obtain $=(x^{\frac{1}{2}})^{\frac{1}{4}}$ Use rule (3) above to obtain: $=x^{\frac{1}{2} \cdot \frac{1}{4}} \\=x^{\frac{1}{8}}$ Use rule (1) to obtain: $=\sqrt[8]{x}$

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