Simplify sixth root of x* square root of x

$\sqrt[6]{x} \cdot \sqrt{x}$

Multiply $\sqrt[6]{x} \sqrt{x}$ .

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

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

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

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

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

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

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

Combine using the product rule for radicals.

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

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

Multiply $x$ by $x^{3}$ .

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

$\sqrt[6]{x^{1} x^{3}}$

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

$\sqrt[6]{x^{1 + 3}}$

Add $1$ and $3$ .

$\sqrt[6]{x^{4}}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

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

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

Pull terms out from under the radical, assuming positive real numbers.

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