Simplify square root of x^3* cube root of x

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

Step 1

Factor out $x^{2}$ .

$\sqrt{x^{2} x} \cdot \sqrt[3]{x}$

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $x \sqrt{x} \sqrt[3]{x}$ .

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

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

$x (x^{\frac{1}{3}} \sqrt{x})$

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

$x (x^{\frac{2}{6}} \sqrt{x})$

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

$x (\sqrt[6]{x^{2}} \sqrt{x})$

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

$x (\sqrt[6]{x^{2}} x^{\frac{1}{2}})$

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

$x (\sqrt[6]{x^{2}} x^{\frac{3}{6}})$

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

$x (\sqrt[6]{x^{2}} \sqrt[6]{x^{3}})$

Combine using the product rule for radicals.

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

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

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

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

Add $2$ and $3$ .

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