Answer
$\sqrt[10]{x^9}$
Work Step by Step
RECALL:
(i) $\sqrt[n]{a} = a^{\frac{1}{n}}$
(ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$
(iii) $(ab)^m = a^mb^m$
(iv) $(a^m)^n=a^{mn}$
(v) $a^m \cdot a^n = a^{m+n}$
Use rules (i) and (ii) above to obtain:
$=x^{\frac{2}{5}} \cdot x^{\frac{1}{2}}$
Use rule (v) above to obtain:
$=x^{\frac{2}{5}+\frac{1}{2}}
\\=x^{\frac{4}{10} + \frac{5}{10}}
\\=x^{\frac{9}{10}}$
Use rule (ii) to obtain:
$\\=\sqrt[10]{x^9}$
