Simplify 15 root of (x^3)/(x^-2)

$\sqrt[15]{\frac{x^{3}}{x^{- 2}}}$

Reduce the expression by cancelling the common factors.

Move $x^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[15]{x^{3} x^{2}}$

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

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

$\sqrt[15]{x^{3 + 2}}$

Add $3$ and $2$ .

$\sqrt[15]{x^{5}}$

Rewrite $\sqrt[15]{x^{5}}$ as $\sqrt[3]{\sqrt[5]{x^{5}}}$ .

$\sqrt[3]{\sqrt[5]{x^{5}}}$

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

$\sqrt[3]{x}$