Algebra Examples

$\sqrt[4]{\frac{\sqrt{m} \sqrt[3]{n^{2}}}{\sqrt{p^{5}}}}$

Step 1

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

$\sqrt[4]{\frac{m^{\frac{1}{2}} \sqrt[3]{n^{2}}}{\sqrt{p^{5}}}}$

Step 2

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

$\sqrt[4]{\frac{m^{\frac{1}{2}} n^{\frac{2}{3}}}{\sqrt{p^{5}}}}$

Step 3

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{p^{5}}$ as $p^{\frac{5}{2}}$ .

$\sqrt[4]{\frac{m^{\frac{1}{2}} n^{\frac{2}{3}}}{p^{\frac{5}{2}}}}$

Step 4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{\frac{m^{\frac{1}{2}} n^{\frac{2}{3}}}{p^{\frac{5}{2}}}}$ as ${(\frac{m^{\frac{1}{2}} n^{\frac{2}{3}}}{p^{\frac{5}{2}}})}^{\frac{1}{4}}$ .

${(\frac{m^{\frac{1}{2}} n^{\frac{2}{3}}}{p^{\frac{5}{2}}})}^{\frac{1}{4}}$