Simplify fourth root of x* square root of x

$\sqrt[4]{x} \cdot \sqrt{x}$

Step 1

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

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

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

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

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

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

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

Step 2

Combine using the product rule for radicals.

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

Step 3

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

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

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

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

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

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

Add $1$ and $2$ .

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