Simplify fourth root of k square root of k

$\sqrt[4]{k} \sqrt{k}$

Step 1

Rewrite the expression using the least common index of $4$ .

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

$\sqrt[4]{k} k^{\frac{1}{2}}$

Rewrite $k^{\frac{1}{2}}$ as $k^{\frac{2}{4}}$ .

$\sqrt[4]{k} k^{\frac{2}{4}}$

Rewrite $k^{\frac{2}{4}}$ as $\sqrt[4]{k^{2}}$ .

$\sqrt[4]{k} \sqrt[4]{k^{2}}$

Step 2

Combine using the product rule for radicals.

$\sqrt[4]{k \cdot k^{2}}$

Step 3

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

Multiply $k$ by $k^{2}$ .

Raise $k$ to the power of $1$ .

$\sqrt[4]{k^{1} k^{2}}$

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

$\sqrt[4]{k^{1 + 2}}$

Add $1$ and $2$ .

$\sqrt[4]{k^{3}}$