[tex]\bf \sqrt[3]{0.027y^9}\qquad
\begin{cases}
0.027=\frac{0027}{1000}\\
27=3^3\\
1000=10^3\\
y^9=(y^3)^3
\end{cases}\qquad \sqrt[3]{\cfrac{27}{1000}y^9}\implies \sqrt[3]{\cfrac{3^3}{10^3}(y^3)^3}
\\\\\\
\sqrt[3]{\cfrac{3^3(y^3)^3}{10^3}}\implies \cfrac{\sqrt[3]{3^3(y^3)^3}}{\sqrt[3]{10^3}}\implies \cfrac{3y^3}{10}\implies 0.3y^3[/tex]
