# Chapter P - Section P.3 - Radicals and Rational Exponents - Exercise Set - Page 46: 108

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

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

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