Simplify ninth root of x^-2*x^5

$\sqrt[9]{x^{- 2} \cdot x^{5}}$

Step 1

Multiply $x^{- 2}$ by $x^{5}$ by adding the exponents.

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

$\sqrt[9]{x^{- 2 + 5}}$

Add $- 2$ and $5$ .

$\sqrt[9]{x^{3}}$

Step 2

Rewrite $\sqrt[9]{x^{3}}$ as $\sqrt[3]{\sqrt[3]{x^{3}}}$ .

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

Step 3

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

$\sqrt[3]{x}$