Algebra Examples

$125^{- \frac{4}{3}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{125^{\frac{4}{3}}}$

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

$\frac{1}{5^{4}}$

Step 2.4

Raise $5$ to the power of $4$ .

$\frac{1}{625}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{625}$

Decimal Form:

$0.0016$