Simplify the Radical Expression square root of x* fourth root of x

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

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

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

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

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

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

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

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

Combine using the product rule for radicals.

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

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

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

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

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

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

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

Add $2$ and $1$ .

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