Finite Math Examples

$\frac{\sqrt[3]{- 7 x^{6} y^{4}}}{\sqrt[3]{448 y^{3}}}$

Step 1

Combine $\sqrt[3]{- 7 x^{6} y^{4}}$ and $\sqrt[3]{448 y^{3}}$ into a single radical.

$\sqrt[3]{\frac{- 7 x^{6} y^{4}}{448 y^{3}}}$

Step 2

Reduce the expression $\frac{- 7 x^{6} y^{4}}{448 y^{3}}$ by cancelling the common factors.

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Step 2.1

Factor $7$ out of $- 7 x^{6} y^{4}$ .

$\sqrt[3]{\frac{7 (- x^{6} y^{4})}{448 y^{3}}}$

Step 2.2

Factor $7$ out of $448 y^{3}$ .

$\sqrt[3]{\frac{7 (- x^{6} y^{4})}{7 (64 y^{3})}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{7 (- x^{6} y^{4})}{7 (64 y^{3})}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{- x^{6} y^{4}}{64 y^{3}}}$

Step 3

Cancel the common factor of $y^{4}$ and $y^{3}$ .

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Step 3.1

Factor $y^{3}$ out of $- x^{6} y^{4}$ .

$\sqrt[3]{\frac{y^{3} (- x^{6} y)}{64 y^{3}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y^{3}$ out of $64 y^{3}$ .

$\sqrt[3]{\frac{y^{3} (- x^{6} y)}{y^{3} \cdot 64}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[3]{\frac{y^{3} (- x^{6} y)}{y^{3} \cdot 64}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[3]{\frac{- x^{6} y}{64}}$

Step 4

Move the negative in front of the fraction.

$\sqrt[3]{- \frac{x^{6} y}{64}}$

Step 5

Rewrite $- \frac{x^{6} y}{64}$ as ${(- \frac{x^{2}}{4})}^{3} y$ .

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Step 5.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$\sqrt[3]{{(- 1)}^{3} \frac{x^{6} y}{64}}$

Step 5.2

Factor the perfect power ${(x^{2})}^{3}$ out of $x^{6} y$ .

$\sqrt[3]{{(- 1)}^{3} \frac{{(x^{2})}^{3} y}{64}}$

Step 5.3

Factor the perfect power $4^{3}$ out of $64$ .

$\sqrt[3]{{(- 1)}^{3} \frac{{(x^{2})}^{3} y}{4^{3} \cdot 1}}$

Step 5.4

Rearrange the fraction $\frac{{(x^{2})}^{3} y}{4^{3} \cdot 1}$ .

$\sqrt[3]{{(- 1)}^{3} ({(\frac{x^{2}}{4})}^{3} y)}$

Step 5.5

Rewrite ${(- 1)}^{3} {(\frac{x^{2}}{4})}^{3}$ as ${(- \frac{x^{2}}{4})}^{3}$ .

$\sqrt[3]{{(- \frac{x^{2}}{4})}^{3} y}$

Step 6

Pull terms out from under the radical.

$- \frac{x^{2}}{4} \sqrt[3]{y}$

Step 7

Combine $\sqrt[3]{y}$ and $\frac{x^{2}}{4}$ .

$- \frac{\sqrt[3]{y} x^{2}}{4}$