Answer
$2a^{\frac{7}{6}}$
Work Step by Step
RECALL:
(i) $a^{-m} = \dfrac{1}{a^m}$
(ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$
(iii) $a^m \cdot a^n = a^{m+n}$
Use rule (ii) above to obtain:
$=2a^{\frac{1}{2}} \cdot a^{\frac{2}{3}}
\\=2\cdot a^{\frac{1}{2}}\cdot a^{\frac{2}{3}}$
Use rule (iii) above to to obtain:
$=2\cdot a^{\frac{1}{2} + \frac{2}{3}}
\\=2a^{\frac{3}{6} + \frac{4}{6}}
\\=2a^{\frac{7}{6}}$
