Simplify cube root of k square root of k

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

Step 1

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

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

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

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

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

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

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

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

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

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

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

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

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

Step 2

Combine using the product rule for radicals.

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

Step 3

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

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

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

Add $2$ and $3$ .

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