Answer
$\sqrt[3]{xy^2}$
Work Step by Step
RECALL:
(i) $\sqrt[n]{a} = a^{\frac{1}{n}}.$
(ii) $(a^m)^n=a^{mn}.$
Use rule (i) above to obtain
$(x^4y^8)^{\frac{1}{12}}.$
Use rule (ii) above to obtain
$x^{\frac{4}{12}}y^{\frac{8}{12}}
\\=x^{\frac{1}{3}}y^{\frac{2}{3}}
\\=(xy^2)^{\frac{1}{3}}.$
Write the expression in radical form using rule (i) above to obtain
$\sqrt[3]{xy^2}.$
