Algebra Examples

${(\frac{27}{125})}^{\frac{- 1}{3}}$

Step 1

Move the negative in front of the fraction.

${(\frac{27}{125})}^{- \frac{1}{3}}$

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{125}{27})}^{\frac{1}{3}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[3]{{(\frac{125}{27})}^{1}}$

Step 4

Anything raised to $1$ is the base itself.

$\sqrt[3]{\frac{125}{27}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{\frac{125}{27}}$

Decimal Form:

$1.\overline{6}$