Algebra Examples

$(\frac{1}{125^{\frac{2}{3}}})$

Step 1

Rewrite $125$ as $5^{3}$ .

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

Step 2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

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

$\frac{1}{25}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{25}$

Decimal Form:

$0.04$