Algebra Examples

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

Step 1

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

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Step 1.1

Apply the product rule to $- \frac{1}{5}$ .

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

Step 1.2

Apply the product rule to $\frac{1}{5}$ .

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

Step 2

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

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

Step 3

One to any power is one.

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

Step 4

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

$- \frac{1}{125}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{125}$

Decimal Form:

$- 0.008$