Answer
$\sqrt[4]{8a^3}$
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) $(a^m)^n=a^{mn}$
Use the rules above to obtain:
$=\left((2a)^{\frac{1}{8}}\right)^6
\\=(2a)^{\frac{1}{8} \cdot 6}
\\=(2a)^{\frac{3}{4}}
\\=\sqrt[4]{(2a)^3}
\\=\sqrt[4]{2^3a^3}
\\=\sqrt[4]{8a^3}$
