## Precalculus (6th Edition) Blitzer

$\sqrt[3]{xy^2}$
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 $\sqrt[3]{xy^2}.$