Simplify ( cube root of 3)/(2 cube root of -375)

$\frac{\sqrt[3]{3}}{2 \sqrt[3]{- 375}}$

Step 1

Combine $\sqrt[3]{3}$ and $\sqrt[3]{- 375}$ into a single radical.

$\frac{\sqrt[3]{\frac{3}{- 375}}}{2}$

Step 2

Cancel the common factor of $3$ and $- 375$ .

Factor $3$ out of $3$ .

$\frac{\sqrt[3]{\frac{3 (1)}{- 375}}}{2}$

Cancel the common factors.

Factor $3$ out of $- 375$ .

$\frac{\sqrt[3]{\frac{3 \cdot 1}{3 \cdot - 125}}}{2}$

Cancel the common factor.

$\frac{\sqrt[3]{\frac{3 \cdot 1}{3 \cdot - 125}}}{2}$

Rewrite the expression.

$\frac{\sqrt[3]{\frac{1}{- 125}}}{2}$

Step 3

Simplify the numerator.

Move the negative in front of the fraction.

$\frac{\sqrt[3]{- \frac{1}{125}}}{2}$

Rewrite $- \frac{1}{125}$ as ${(- \frac{1}{5})}^{3}$ .

$\frac{\sqrt[3]{{(- \frac{1}{5})}^{3}}}{2}$

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

$\frac{- \frac{1}{5}}{2}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- \frac{1}{5} \cdot \frac{1}{2}$

Step 5

Multiply $- \frac{1}{5} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{1}{5}$ .

$- \frac{1}{2 \cdot 5}$

Multiply $2$ by $5$ .

$- \frac{1}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{10}$

Decimal Form:

$- 0.1$