Answer
$2a^2$
Work Step by Step
RECALL:
(i) $\sqrt[n]{a} = a^{\frac{1}{n}}$
(ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$
(iii) $(ab)^m = a^mb^m$
Use rule (i) above to obtain:
$=(8a^6)^{\frac{1}{3}}$
Use rule (iii) above to obtain:
$=8^{\frac{1}{3}}(a^6)^{\frac{1}{3}}
\\=(2^3)^{\frac{1}{3}}a^{6\cdot \frac{1}{3}}
\\=2^{3 \cdot \frac{1}{3}} a^2
\\=2^1a^2
\\=2a^2$
