Evaluate -(-2/5)^3

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

Step 1

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

Apply the product rule to $- \frac{2}{5}$ .

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

Apply the product rule to $\frac{2}{5}$ .

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

Step 2

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

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

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

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

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

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $3$ and $1$ .

${(- 1)}^{4} \frac{2^{3}}{5^{3}}$

Step 3

Raise $- 1$ to the power of $4$ .

$1 \frac{2^{3}}{5^{3}}$

Step 4

Multiply $\frac{2^{3}}{5^{3}}$ by $1$ .

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

Step 5

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

$\frac{8}{5^{3}}$

Step 6

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

$\frac{8}{125}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{125}$

Decimal Form:

$0.064$