Answer
$3a^4$
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) $(a^m)^n=a^{mn}$
Write $27$ as $3^3$ to obtain:
$=\sqrt[3]{3^3a^{12}}$
Use rule (i) to obtain:
$=(3^3a^{12})^{\frac{1}{3}}$
Use rule (iii) above to obtain:
$=(3^3)^{\frac{1}{3}} \cdot (a^{12})^{\frac{1}{3}}$
Use rule (iv) above to obtain:
$=3^{3\cdot\frac{1}{3}} \cdot a^{12 \cdot \frac{1}{3}}
\\=3^1\cdot a^{4}
\\=3a^4$
