Basic Math Examples

$\frac{\sqrt[3]{81 z^{13} y^{15}}}{\sqrt[3]{8 z^{9} y^{7}}}$

Step 1

Combine $\sqrt[3]{81 z^{13} y^{15}}$ and $\sqrt[3]{8 z^{9} y^{7}}$ into a single radical.

$\sqrt[3]{\frac{81 z^{13} y^{15}}{8 z^{9} y^{7}}}$

Step 2

Reduce the expression $\frac{81 z^{13} y^{15}}{8 z^{9} y^{7}}$ by cancelling the common factors.

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Step 2.1

Factor $z^{9}$ out of $81 z^{13} y^{15}$ .

$\sqrt[3]{\frac{z^{9} (81 z^{4} y^{15})}{8 z^{9} y^{7}}}$

Step 2.2

Factor $z^{9}$ out of $8 z^{9} y^{7}$ .

$\sqrt[3]{\frac{z^{9} (81 z^{4} y^{15})}{z^{9} (8 y^{7})}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{z^{9} (81 z^{4} y^{15})}{z^{9} (8 y^{7})}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{81 z^{4} y^{15}}{8 y^{7}}}$

Step 3

Cancel the common factor of $y^{15}$ and $y^{7}$ .

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Step 3.1

Factor $y^{7}$ out of $81 z^{4} y^{15}$ .

$\sqrt[3]{\frac{y^{7} (81 z^{4} y^{8})}{8 y^{7}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y^{7}$ out of $8 y^{7}$ .

$\sqrt[3]{\frac{y^{7} (81 z^{4} y^{8})}{y^{7} \cdot 8}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[3]{\frac{y^{7} (81 z^{4} y^{8})}{y^{7} \cdot 8}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[3]{\frac{81 z^{4} y^{8}}{8}}$

Step 4

Rewrite $\frac{81 z^{4} y^{8}}{8}$ as ${(\frac{3 z y^{2}}{2})}^{3} (3 z y^{2})$ .

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Step 4.1

Factor the perfect power $2^{3}$ out of $8$ .

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

Step 4.2

Rearrange the fraction $\frac{{(3 z y^{2})}^{3} \cdot (3 z y^{2})}{2^{3} \cdot 1}$ .

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

Step 5

Pull terms out from under the radical.

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

Step 6

Combine $\frac{3 z y^{2}}{2}$ and $\sqrt[3]{3 z y^{2}}$ .

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