Answer
$\sqrt[8]{x}$
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:
$=\sqrt[8]{x}$
