Precalculus Examples

$\sqrt[3]{a^{2} b^{3}} \sqrt[3]{a^{10} b}$

Step 1

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

${(a^{2} b^{3})}^{\frac{1}{3}} \sqrt[3]{a^{10} b}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{a^{10} b}$ as ${(a^{10} b)}^{\frac{1}{3}}$ .

${(a^{2} b^{3})}^{\frac{1}{3}} {(a^{10} b)}^{\frac{1}{3}}$