Answer
$\sqrt[6]{a^5}$
Work Step by Step
RECALL:
(i) $a^m \cdot a^n = a^{m+n}$
(ii) $\sqrt[n]{a} = a^{\frac{1}{n}}$
(iii) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$
Use rule (ii) to have:
$=a^{\frac{1}{2}}\cdot a^{\frac{1}{3}}$
Use rule (i) to have:
$\\=a^{\frac{1}{2} + \frac{1}{3}}
\\=a^{\frac{3}{6} + \frac{2}{6}}
\\=a^{\frac{5}{6}}$
Use rule (iii) to have:
$=\sqrt[6]{a^5}$
