Pre-Algebra Examples

$\frac{\sqrt[3]{16 a^{10} b^{2}}}{\sqrt[3]{2 a^{5} b^{- 4}}}$

Step 1

Combine $\sqrt[3]{16 a^{10} b^{2}}$ and $\sqrt[3]{2 a^{5} b^{- 4}}$ into a single radical.

$\sqrt[3]{\frac{16 a^{10} b^{2}}{2 a^{5} b^{- 4}}}$

Step 2

Reduce the expression $\frac{16 a^{10} b^{2}}{2 a^{5} b^{- 4}}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $16 a^{10} b^{2}$ .

$\sqrt[3]{\frac{2 (8 a^{10} b^{2})}{2 a^{5} b^{- 4}}}$

Step 2.2

Factor $2$ out of $2 a^{5} b^{- 4}$ .

$\sqrt[3]{\frac{2 (8 a^{10} b^{2})}{2 (a^{5} b^{- 4})}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{2 (8 a^{10} b^{2})}{2 (a^{5} b^{- 4})}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{8 a^{10} b^{2}}{a^{5} b^{- 4}}}$

Step 3

Move $b^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[3]{\frac{8 a^{10} b^{2} b^{4}}{a^{5}}}$

Step 4

Multiply $b^{2}$ by $b^{4}$ by adding the exponents.

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Step 4.1

Move $b^{4}$ .

$\sqrt[3]{\frac{8 a^{10} (b^{4} b^{2})}{a^{5}}}$

Step 4.2

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

$\sqrt[3]{\frac{8 a^{10} b^{4 + 2}}{a^{5}}}$

Step 4.3

Add $4$ and $2$ .

$\sqrt[3]{\frac{8 a^{10} b^{6}}{a^{5}}}$

Step 5

Cancel the common factor of $a^{10}$ and $a^{5}$ .

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Step 5.1

Factor $a^{5}$ out of $8 a^{10} b^{6}$ .

$\sqrt[3]{\frac{a^{5} (8 a^{5} b^{6})}{a^{5}}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$\sqrt[3]{\frac{a^{5} (8 a^{5} b^{6})}{a^{5} \cdot 1}}$

Step 5.2.2

Cancel the common factor.

$\sqrt[3]{\frac{a^{5} (8 a^{5} b^{6})}{a^{5} \cdot 1}}$

Step 5.2.3

Rewrite the expression.

$\sqrt[3]{\frac{8 a^{5} b^{6}}{1}}$

Step 5.2.4

Divide $8 a^{5} b^{6}$ by $1$ .

$\sqrt[3]{8 a^{5} b^{6}}$

Step 6

Rewrite $8 a^{5} b^{6}$ as ${(2 a b^{2})}^{3} a^{2}$ .

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Step 6.1

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} a^{5} b^{6}}$

Step 6.2

Factor out $a^{3}$ .

$\sqrt[3]{2^{3} (a^{3} a^{2}) b^{6}}$

Step 6.3

Rewrite $b^{6}$ as ${(b^{2})}^{3}$ .

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

Step 6.4

Move $a^{2}$ .

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

Step 6.5

Rewrite $2^{3} (a^{3}) {(b^{2})}^{3}$ as ${(2 a b^{2})}^{3}$ .

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

Step 7

Pull terms out from under the radical.

$2 a b^{2} \sqrt[3]{a^{2}}$