Simplify (-8/125)^(-1/3)

${(- \frac{8}{125})}^{\frac{- 1}{3}}$

Move the negative in front of the fraction.

${(- \frac{8}{125})}^{- \frac{1}{3}}$

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

${(- \frac{125}{8})}^{\frac{1}{3}}$

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

Apply the product rule to $- \frac{125}{8}$ .

${(- 1)}^{\frac{1}{3}} {(\frac{125}{8})}^{\frac{1}{3}}$

Apply the product rule to $\frac{125}{8}$ .

${(- 1)}^{\frac{1}{3}} \frac{125^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Simplify the expression.

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${({(- 1)}^{3})}^{\frac{1}{3}} \frac{125^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

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

${(- 1)}^{3 (\frac{1}{3})} \frac{125^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(- 1)}^{3 (\frac{1}{3})} \frac{125^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Rewrite the expression.

${(- 1)}^{1} \frac{125^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Evaluate the exponent.

$- \frac{125^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

Simplify the numerator.

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

$- \frac{{(5^{3})}^{\frac{1}{3}}}{8^{\frac{1}{3}}}$

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

$- \frac{5^{3 (\frac{1}{3})}}{8^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- \frac{5^{3 (\frac{1}{3})}}{8^{\frac{1}{3}}}$

Rewrite the expression.

$- \frac{5^{1}}{8^{\frac{1}{3}}}$

Evaluate the exponent.

$- \frac{5}{8^{\frac{1}{3}}}$

Simplify the denominator.

Rewrite $8$ as $2^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$- \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{2}$

Decimal Form:

$- 2.5$

Mixed Number Form:

$- 2 \frac{1}{2}$

Simplify (-8/125)^(-1/3)

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