Simplify cube root of x square root of x

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

Step 1

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 $x^{\frac{1}{3}}$ .

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

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

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

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

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

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

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

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

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

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

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

Step 2

Combine using the product rule for radicals.

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

Step 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.

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

Add $2$ and $3$ .

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