Simplify ( cube root of -15)/(5 cube root of 5)

$\frac{\sqrt[3]{- 15}}{5 \sqrt[3]{5}}$

Step 1

Combine $\sqrt[3]{- 15}$ and $\sqrt[3]{5}$ into a single radical.

$\frac{\sqrt[3]{\frac{- 15}{5}}}{5}$

Step 2

Cancel the common factor of $- 15$ and $5$ .

Factor $5$ out of $- 15$ .

$\frac{\sqrt[3]{\frac{5 \cdot - 3}{5}}}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

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

Cancel the common factor.

$\frac{\sqrt[3]{\frac{5 \cdot - 3}{5 \cdot 1}}}{5}$

Rewrite the expression.

$\frac{\sqrt[3]{\frac{- 3}{1}}}{5}$

Divide $- 3$ by $1$ .

$\frac{\sqrt[3]{- 3}}{5}$

Step 3

Simplify the numerator.

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

Rewrite $- 3$ as $- 1 (3)$ .

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

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

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

Pull terms out from under the radical.

$\frac{- 1 \sqrt[3]{3}}{5}$

Rewrite $- 1 \sqrt[3]{3}$ as $- \sqrt[3]{3}$ .

$\frac{- \sqrt[3]{3}}{5}$

Step 4

Move the negative in front of the fraction.

$- \frac{\sqrt[3]{3}}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt[3]{3}}{5}$

Decimal Form:

$- 0.28844991 \dots$