Answer
$\sqrt[3]{x^2y}$
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
$(x^6y^3)^{\frac{1}{9}}.$
Use rule (ii) above to obtain
$x^{\frac{6}{9}}y^{\frac{3}{9}}
\\=x^{\frac{2}{3}}y^{\frac{1}{3}}
\\=(x^2y)^{\frac{1}{3}}.$
Write the expression in radical form using rule (i) above to obtain
$\sqrt[3]{x^2y}.$
