Simplify fifth root of 15/-32

$\sqrt[5]{\frac{15}{- 32}}$

Step 1

Move the negative in front of the fraction.

$\sqrt[5]{- \frac{15}{32}}$

Step 2

Rewrite $- \frac{15}{32}$ as ${(- \frac{1}{2})}^{5} \cdot 15$ .

Rewrite $- 1$ as ${(- 1)}^{5}$ .

$\sqrt[5]{{(- 1)}^{5} \frac{15}{32}}$

Factor the perfect power $1^{5}$ out of $15$ .

$\sqrt[5]{{(- 1)}^{5} \frac{1^{5} \cdot 15}{32}}$

Factor the perfect power $2^{5}$ out of $32$ .

$\sqrt[5]{{(- 1)}^{5} \frac{1^{5} \cdot 15}{2^{5} \cdot 1}}$

Rearrange the fraction $\frac{1^{5} \cdot 15}{2^{5} \cdot 1}$ .

$\sqrt[5]{{(- 1)}^{5} ({(\frac{1}{2})}^{5} \cdot 15)}$

Rewrite ${(- 1)}^{5} {(\frac{1}{2})}^{5}$ as ${(- \frac{1}{2})}^{5}$ .

$\sqrt[5]{{(- \frac{1}{2})}^{5} \cdot 15}$

Step 3

Pull terms out from under the radical.

$- \frac{1}{2} \sqrt[5]{15}$

Step 4

Combine $\sqrt[5]{15}$ and $\frac{1}{2}$ .

$- \frac{\sqrt[5]{15}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt[5]{15}}{2}$

Decimal Form:

$- 0.85938596 \dots$