Algebra Examples

$\frac{3 \sqrt[5]{64 x^{10} y^{3}}}{\sqrt[5]{2 x^{3} y^{- 7}}}$

Step 1

Combine $\sqrt[5]{64 x^{10} y^{3}}$ and $\sqrt[5]{2 x^{3} y^{- 7}}$ into a single radical.

$3 \sqrt[5]{\frac{64 x^{10} y^{3}}{2 x^{3} y^{- 7}}}$

Step 2

Reduce the expression $\frac{64 x^{10} y^{3}}{2 x^{3} y^{- 7}}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $64 x^{10} y^{3}$ .

$3 \sqrt[5]{\frac{2 (32 x^{10} y^{3})}{2 x^{3} y^{- 7}}}$

Step 2.2

Factor $2$ out of $2 x^{3} y^{- 7}$ .

$3 \sqrt[5]{\frac{2 (32 x^{10} y^{3})}{2 (x^{3} y^{- 7})}}$

Step 2.3

Cancel the common factor.

$3 \sqrt[5]{\frac{2 (32 x^{10} y^{3})}{2 (x^{3} y^{- 7})}}$

Step 2.4

Rewrite the expression.

$3 \sqrt[5]{\frac{32 x^{10} y^{3}}{x^{3} y^{- 7}}}$

Step 3

Move $y^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3 \sqrt[5]{\frac{32 x^{10} y^{3} y^{7}}{x^{3}}}$

Step 4

Multiply $y^{3}$ by $y^{7}$ by adding the exponents.

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Step 4.1

Move $y^{7}$ .

$3 \sqrt[5]{\frac{32 x^{10} (y^{7} y^{3})}{x^{3}}}$

Step 4.2

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

$3 \sqrt[5]{\frac{32 x^{10} y^{7 + 3}}{x^{3}}}$

Step 4.3

Add $7$ and $3$ .

$3 \sqrt[5]{\frac{32 x^{10} y^{10}}{x^{3}}}$

Step 5

Cancel the common factor of $x^{10}$ and $x^{3}$ .

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Step 5.1

Factor $x^{3}$ out of $32 x^{10} y^{10}$ .

$3 \sqrt[5]{\frac{x^{3} (32 x^{7} y^{10})}{x^{3}}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$3 \sqrt[5]{\frac{x^{3} (32 x^{7} y^{10})}{x^{3} \cdot 1}}$

Step 5.2.2

Cancel the common factor.

$3 \sqrt[5]{\frac{x^{3} (32 x^{7} y^{10})}{x^{3} \cdot 1}}$

Step 5.2.3

Rewrite the expression.

$3 \sqrt[5]{\frac{32 x^{7} y^{10}}{1}}$

Step 5.2.4

Divide $32 x^{7} y^{10}$ by $1$ .

$3 \sqrt[5]{32 x^{7} y^{10}}$

Step 6

Rewrite $32 x^{7} y^{10}$ as ${(2 x y^{2})}^{5} x^{2}$ .

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Step 6.1

Rewrite $32$ as $2^{5}$ .

$3 \sqrt[5]{2^{5} x^{7} y^{10}}$

Step 6.2

Factor out $x^{5}$ .

$3 \sqrt[5]{2^{5} (x^{5} x^{2}) y^{10}}$

Step 6.3

Rewrite $y^{10}$ as ${(y^{2})}^{5}$ .

$3 \sqrt[5]{2^{5} (x^{5} x^{2}) {(y^{2})}^{5}}$

Step 6.4

Move $x^{2}$ .

$3 \sqrt[5]{2^{5} (x^{5}) {(y^{2})}^{5} x^{2}}$

Step 6.5

Rewrite $2^{5} (x^{5}) {(y^{2})}^{5}$ as ${(2 x y^{2})}^{5}$ .

$3 \sqrt[5]{{(2 x y^{2})}^{5} x^{2}}$

Step 7

Pull terms out from under the radical.

$3 (2 x y^{2} \sqrt[5]{x^{2}})$

Step 8

Multiply $2$ by $3$ .

$6 x y^{2} \sqrt[5]{x^{2}}$