Basic Math Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

Rewrite

$- \frac{88}{27}$ as

${(- \frac{2}{3})}^{3} \cdot 11$ .

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Step 2.1

Rewrite

$- 1$ as

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

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

Step 2.2

Factor the perfect power

$2^{3}$ out of

$88$ .

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

Step 2.3

Factor the perfect power

$3^{3}$ out of

$27$ .

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

Step 2.4

Rearrange the fraction

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

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

Step 2.5

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:

$- 1.48265339 \dots$