Algebra Examples

$\sqrt[33]{\frac{1}{u^{- 3} \cdot u^{- 8}}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Move $u^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[33]{\frac{u^{3}}{u^{- 8}}}$

Step 1.2

Move $u^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[33]{u^{3} u^{8}}$

Step 1.3

Multiply $u^{3}$ by $u^{8}$ by adding the exponents.

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Step 1.3.1

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

$\sqrt[33]{u^{3 + 8}}$

Step 1.3.2

Add $3$ and $8$ .

$\sqrt[33]{u^{11}}$

Step 2

Rewrite $\sqrt[33]{u^{11}}$ as $\sqrt[3]{\sqrt[11]{u^{11}}}$ .

$\sqrt[3]{\sqrt[11]{u^{11}}}$

Step 3

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

$\sqrt[3]{u}$