Precalculus Examples

$(a b \sqrt[3]{2 a^{2} b^{2}}) (2 a \sqrt[3]{4 a b^{2}})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 a^{2} b^{2}}$ as ${(2 a^{2} b^{2})}^{\frac{1}{3}}$ .

$a b {(2 a^{2} b^{2})}^{\frac{1}{3}} (2 a \sqrt[3]{4 a b^{2}})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 a b^{2}}$ as ${(4 a b^{2})}^{\frac{1}{3}}$ .

$a b {(2 a^{2} b^{2})}^{\frac{1}{3}} (2 a {(4 a b^{2})}^{\frac{1}{3}})$