Algebra Examples

$\sqrt[3]{\frac{8 x^{6} y^{9}}{27 y^{3} z^{3}}}$

Step 1

Reduce the expression $\frac{8 x^{6} y^{9}}{27 y^{3} z^{3}}$ by cancelling the common factors.

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Step 1.1

Factor $y^{3}$ out of $8 x^{6} y^{9}$ .

$\sqrt[3]{\frac{y^{3} (8 x^{6} y^{6})}{27 y^{3} z^{3}}}$

Step 1.2

Factor $y^{3}$ out of $27 y^{3} z^{3}$ .

$\sqrt[3]{\frac{y^{3} (8 x^{6} y^{6})}{y^{3} (27 z^{3})}}$

Step 1.3

Cancel the common factor.

$\sqrt[3]{\frac{y^{3} (8 x^{6} y^{6})}{y^{3} (27 z^{3})}}$

Step 1.4

Rewrite the expression.

$\sqrt[3]{\frac{8 x^{6} y^{6}}{27 z^{3}}}$

Step 2

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

$\sqrt[3]{\frac{{(2 x^{2} y^{2})}^{3}}{27 z^{3}}}$

Step 3

Rewrite $27 z^{3}$ as ${(3 z)}^{3}$ .

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

Step 4

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

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

Step 5

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

$\frac{2 x^{2} y^{2}}{3 z}$