Basic Math Examples

${(\frac{- 2}{3})}^{5}$

Step 1

Move the negative in front of the fraction.

${(- \frac{2}{3})}^{5}$

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

${(- 1)}^{5} {(\frac{2}{3})}^{5}$

Step 2.2

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

${(- 1)}^{5} \frac{2^{5}}{3^{5}}$

Step 3

Raise $- 1$ to the power of $5$ .

$- \frac{2^{5}}{3^{5}}$

Step 4

Raise $2$ to the power of $5$ .

$- \frac{32}{3^{5}}$

Step 5

Raise $3$ to the power of $5$ .

$- \frac{32}{243}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{32}{243}$

Decimal Form:

$- 0.13168724 \dots$