Algebra Examples

${(- \frac{2}{3})}^{- 3}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(- \frac{3}{2})}^{3}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $- \frac{3}{2}$ .

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

Step 2.2

Apply the product rule to $\frac{3}{2}$ .

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

Step 3

Raise $- 1$ to the power of $3$ .

$- \frac{3^{3}}{2^{3}}$

Step 4

Raise $3$ to the power of $3$ .

$- \frac{27}{2^{3}}$

Step 5

Raise $2$ to the power of $3$ .

$- \frac{27}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{27}{8}$

Decimal Form:

$- 3.375$

Mixed Number Form:

$- 3 \frac{3}{8}$