Answer
$\sqrt[3]{x^2y}$
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) $(a^m)^n=a^{mn}$
(v) $\sqrt {a} \sqrt{b}= \sqrt{ab}$
Use the rules above to obtain:
$=\left(x^6y^3\right)^{\frac{1}{9}}
\\=(x^6)^{\frac{1}{9}}(y^3)^{\frac{1}{9}}
\\=x^{6 \cdot \frac{1}{9}} \cdot y^{3\cdot\frac{1}{9}}
\\=x^{\frac{2}{3}} \cdot y^{\frac{1}{3}}
\\=\sqrt[3]{x^2} \cdot \sqrt[3]{y}
\\=\sqrt[3]{x^2y}$
