Question

Simplify the radical expression ^3sqrt 125x^9 y^12

Answer 1

$\bf \sqrt[3]{125x^9y^{12}}~~ \begin{cases} 125=5\cdot 5\cdot 5\\ \qquad 5^3\\ x^9=x^{3\cdot 3}\\ \qquad (x^3)^3\\ y^{12}=y^{4\cdot 3}\\ \qquad (y^4)^3 \end{cases}\implies \sqrt[3]{5^3(x^3)^3(y^4)^3}\implies 5x^3y^4$