Algebra Examples

$\frac{\sqrt[3]{2}}{\sqrt[3]{- 128}}$

Step 1

Combine $\sqrt[3]{2}$ and $\sqrt[3]{- 128}$ into a single radical.

$\sqrt[3]{\frac{2}{- 128}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $2$ and $- 128$ .

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Step 2.1.1

Factor $2$ out of $2$ .

$\sqrt[3]{\frac{2 (1)}{- 128}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $- 128$ .

$\sqrt[3]{\frac{2 \cdot 1}{2 \cdot - 64}}$

Step 2.1.2.2

Cancel the common factor.

$\sqrt[3]{\frac{2 \cdot 1}{2 \cdot - 64}}$

Step 2.1.2.3

Rewrite the expression.

$\sqrt[3]{\frac{1}{- 64}}$

Step 2.2

Move the negative in front of the fraction.

$\sqrt[3]{- \frac{1}{64}}$

Step 3

Rewrite $- \frac{1}{64}$ as ${(- \frac{1}{4})}^{3}$ .

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

Step 4

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

$- \frac{1}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{4}$

Decimal Form:

$- 0.25$