Question

Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. 

Answer 1

$\sqrt{96x^2y}=\sqrt{16\cdot6\cdot x^2\cdot y}=\sqrt{16}\cdot\sqrt6\cdot\sqrt{x^2}\cdot\sqrt{y}\\\\=4\cdot\sqrt6\cdot x\cdot\sqrt{y}=4x\sqrt{6y}$

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$\left(x^4y^4\right)^\frac{1}{3}=\left(x^4\right)^\frac{1}{3}\left(y^4\right)^\frac{1}{3}=x^{4\cdot\frac{1}{3}}y^{4\cdot\frac{1}{3}}=x^\frac{4}{3}y^\frac{4}{3}=x^{1+\frac{1}{3}}y^{1+\frac{1}{3}}\\\\=x^1x^\frac{1}{3}y^1y^\frac{1}{3}=x\sqrt[3]{x}\cdot y\sqrt[3]y=xy\sqrt[3]{xy}$