Simplify the Radical Expression fourth root of x* square root of x^3

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

Step 1

Factor out $x^{2}$ .

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

Step 2

Pull terms out from under the radical.

$\sqrt[4]{x} \cdot (| x | \sqrt{x})$

Step 3

Multiply $\sqrt[4]{x} (| x | \sqrt{x})$ .

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

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

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

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

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

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

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

Combine using the product rule for radicals.

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

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

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

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

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

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

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

Add $2$ and $1$ .

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