Evaluate cube root of -88/27

$\sqrt[3]{\frac{- 88}{27}}$

Step 1

Move the negative in front of the fraction.

$\sqrt[3]{- \frac{88}{27}}$

Step 2

Rewrite $- \frac{88}{27}$ as ${(- \frac{2}{3})}^{3} \cdot 11$ .

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

$\sqrt[3]{{(- 1)}^{3} \frac{88}{27}}$

Factor the perfect power $2^{3}$ out of $88$ .

$\sqrt[3]{{(- 1)}^{3} \frac{2^{3} \cdot 11}{27}}$

Factor the perfect power $3^{3}$ out of $27$ .

$\sqrt[3]{{(- 1)}^{3} \frac{2^{3} \cdot 11}{3^{3} \cdot 1}}$

Rearrange the fraction $\frac{2^{3} \cdot 11}{3^{3} \cdot 1}$ .

$\sqrt[3]{{(- 1)}^{3} ({(\frac{2}{3})}^{3} \cdot 11)}$

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

$\sqrt[3]{{(- \frac{2}{3})}^{3} \cdot 11}$

Step 3

Pull terms out from under the radical.

$- \frac{2}{3} \sqrt[3]{11}$

Step 4

Combine $\sqrt[3]{11}$ and $\frac{2}{3}$ .

$- \frac{\sqrt[3]{11} \cdot 2}{3}$

Step 5

Move $2$ to the left of $\sqrt[3]{11}$ .

$- \frac{2 \sqrt[3]{11}}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{2 \sqrt[3]{11}}{3}$

Decimal Form:

$- 1.48265339 \dots$