Algebra Examples

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

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Add $3$ and $2$ .

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

Step 2

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

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

Step 3

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

$\sqrt[3]{x}$