Simplify cube root of m square root of m

$\sqrt[3]{m} \sqrt{m}$

Step 1

Rewrite the expression using the least common index of $6$ .

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

$m^{\frac{1}{3}} \sqrt{m}$

Rewrite $m^{\frac{1}{3}}$ as $m^{\frac{2}{6}}$ .

$m^{\frac{2}{6}} \sqrt{m}$

Rewrite $m^{\frac{2}{6}}$ as $\sqrt[6]{m^{2}}$ .

$\sqrt[6]{m^{2}} \sqrt{m}$

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

$\sqrt[6]{m^{2}} m^{\frac{1}{2}}$

Rewrite $m^{\frac{1}{2}}$ as $m^{\frac{3}{6}}$ .

$\sqrt[6]{m^{2}} m^{\frac{3}{6}}$

Rewrite $m^{\frac{3}{6}}$ as $\sqrt[6]{m^{3}}$ .

$\sqrt[6]{m^{2}} \sqrt[6]{m^{3}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[6]{m^{2} m^{3}}$

Step 3

Multiply $m^{2}$ by $m^{3}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[6]{m^{2 + 3}}$

Add $2$ and $3$ .

$\sqrt[6]{m^{5}}$