Algebra Examples

$6 \sqrt[3]{x^{7} y^{5}} \div 2 \sqrt[3]{x y^{2}}$

Step 1

Rewrite the division as a fraction.

$\frac{6 \sqrt[3]{x^{7} y^{5}}}{2 \sqrt[3]{x y^{2}}}$

Step 2

Cancel the common factor of $6$ and $2$ .

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Step 2.1

Factor $2$ out of $6 \sqrt[3]{x^{7} y^{5}}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2 \sqrt[3]{x y^{2}}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

Reduce the expression $\frac{x^{7} y^{5}}{x y^{2}}$ by cancelling the common factors.

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Step 4.1

Factor $x$ out of $x^{7} y^{5}$ .

$3 \sqrt[3]{\frac{x (x^{6} y^{5})}{x y^{2}}}$

Step 4.2

Factor $x$ out of $x y^{2}$ .

$3 \sqrt[3]{\frac{x (x^{6} y^{5})}{x (y^{2})}}$

Step 4.3

Cancel the common factor.

$3 \sqrt[3]{\frac{x (x^{6} y^{5})}{x y^{2}}}$

Step 4.4

Rewrite the expression.

$3 \sqrt[3]{\frac{x^{6} y^{5}}{y^{2}}}$

Step 5

Cancel the common factor of $y^{5}$ and $y^{2}$ .

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Step 5.1

Factor $y^{2}$ out of $x^{6} y^{5}$ .

$3 \sqrt[3]{\frac{y^{2} (x^{6} y^{3})}{y^{2}}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$3 \sqrt[3]{\frac{y^{2} (x^{6} y^{3})}{y^{2} \cdot 1}}$

Step 5.2.2

Cancel the common factor.

$3 \sqrt[3]{\frac{y^{2} (x^{6} y^{3})}{y^{2} \cdot 1}}$

Step 5.2.3

Rewrite the expression.

$3 \sqrt[3]{\frac{x^{6} y^{3}}{1}}$

Step 5.2.4

Divide $x^{6} y^{3}$ by $1$ .

$3 \sqrt[3]{x^{6} y^{3}}$

Step 6

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

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

Step 7

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

$3 x^{2} y$