Algebra Examples

$\frac{\sqrt[3]{625 x^{10} y^{7} z^{11}}}{\sqrt[3]{5 x^{2} y z^{5}}}$

Step 1

Combine $\sqrt[3]{625 x^{10} y^{7} z^{11}}$ and $\sqrt[3]{5 x^{2} y z^{5}}$ into a single radical.

$\sqrt[3]{\frac{625 x^{10} y^{7} z^{11}}{5 x^{2} y z^{5}}}$

Step 2

Reduce the expression $\frac{625 x^{10} y^{7} z^{11}}{5 x^{2} y z^{5}}$ by cancelling the common factors.

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Step 2.1

Factor $5$ out of $625 x^{10} y^{7} z^{11}$ .

$\sqrt[3]{\frac{5 (125 x^{10} y^{7} z^{11})}{5 x^{2} y z^{5}}}$

Step 2.2

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

$\sqrt[3]{\frac{5 (125 x^{10} y^{7} z^{11})}{5 (x^{2} y z^{5})}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{5 (125 x^{10} y^{7} z^{11})}{5 (x^{2} y z^{5})}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{125 x^{10} y^{7} z^{11}}{x^{2} y z^{5}}}$

Step 3

Cancel the common factor of $x^{10}$ and $x^{2}$ .

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Step 3.1

Factor $x^{2}$ out of $125 x^{10} y^{7} z^{11}$ .

$\sqrt[3]{\frac{x^{2} (125 x^{8} y^{7} z^{11})}{x^{2} y z^{5}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\sqrt[3]{\frac{x^{2} (125 x^{8} y^{7} z^{11})}{x^{2} (y z^{5})}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} (125 x^{8} y^{7} z^{11})}{x^{2} (y z^{5})}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[3]{\frac{125 x^{8} y^{7} z^{11}}{y z^{5}}}$

Step 4

Cancel the common factor of $y^{7}$ and $y$ .

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Step 4.1

Factor $y$ out of $125 x^{8} y^{7} z^{11}$ .

$\sqrt[3]{\frac{y (125 x^{8} y^{6} z^{11})}{y z^{5}}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y$ out of $y z^{5}$ .

$\sqrt[3]{\frac{y (125 x^{8} y^{6} z^{11})}{y (z^{5})}}$

Step 4.2.2

Cancel the common factor.

$\sqrt[3]{\frac{y (125 x^{8} y^{6} z^{11})}{y z^{5}}}$

Step 4.2.3

Rewrite the expression.

$\sqrt[3]{\frac{125 x^{8} y^{6} z^{11}}{z^{5}}}$

Step 5

Cancel the common factor of $z^{11}$ and $z^{5}$ .

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Step 5.1

Factor $z^{5}$ out of $125 x^{8} y^{6} z^{11}$ .

$\sqrt[3]{\frac{z^{5} (125 x^{8} y^{6} z^{6})}{z^{5}}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$\sqrt[3]{\frac{z^{5} (125 x^{8} y^{6} z^{6})}{z^{5} \cdot 1}}$

Step 5.2.2

Cancel the common factor.

$\sqrt[3]{\frac{z^{5} (125 x^{8} y^{6} z^{6})}{z^{5} \cdot 1}}$

Step 5.2.3

Rewrite the expression.

$\sqrt[3]{\frac{125 x^{8} y^{6} z^{6}}{1}}$

Step 5.2.4

Divide $125 x^{8} y^{6} z^{6}$ by $1$ .

$\sqrt[3]{125 x^{8} y^{6} z^{6}}$

Step 6

Rewrite $125 x^{8} y^{6} z^{6}$ as ${(5 x^{2} y^{2} z^{2})}^{3} x^{2}$ .

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Step 6.1

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} x^{8} y^{6} z^{6}}$

Step 6.2

Factor out $x^{6}$ .

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

Step 6.3

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

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

Step 6.4

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

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

Step 6.5

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

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

Step 6.6

Move $x^{2}$ .

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

Step 6.7

Rewrite $5^{3} ({(x^{2})}^{3}) {(y^{2})}^{3} {(z^{2})}^{3}$ as ${(5 x^{2} y^{2} z^{2})}^{3}$ .

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

Step 7

Pull terms out from under the radical.

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