Simplify (-216/125)^(-2/3)

${(- \frac{216}{125})}^{- \frac{2}{3}}$

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

${(- \frac{125}{216})}^{\frac{2}{3}}$

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

Apply the product rule to $- \frac{125}{216}$ .

${(- 1)}^{\frac{2}{3}} {(\frac{125}{216})}^{\frac{2}{3}}$

Apply the product rule to $\frac{125}{216}$ .

${(- 1)}^{\frac{2}{3}} \frac{125^{\frac{2}{3}}}{216^{\frac{2}{3}}}$

Reduce the expression by cancelling the common factors.

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

${({(- 1)}^{3})}^{\frac{2}{3}} \frac{125^{\frac{2}{3}}}{216^{\frac{2}{3}}}$

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

${(- 1)}^{3 (\frac{2}{3})} \frac{125^{\frac{2}{3}}}{216^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(- 1)}^{3 (\frac{2}{3})} \frac{125^{\frac{2}{3}}}{216^{\frac{2}{3}}}$

Rewrite the expression.

${(- 1)}^{2} \frac{125^{\frac{2}{3}}}{216^{\frac{2}{3}}}$

Simplify the expression.

Raise $- 1$ to the power of $2$ .

$1 \frac{125^{\frac{2}{3}}}{216^{\frac{2}{3}}}$

Multiply $\frac{125^{\frac{2}{3}}}{216^{\frac{2}{3}}}$ by $1$ .

$\frac{125^{\frac{2}{3}}}{216^{\frac{2}{3}}}$

Simplify the numerator.

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

$\frac{{(5^{3})}^{\frac{2}{3}}}{216^{\frac{2}{3}}}$

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

$\frac{5^{3 (\frac{2}{3})}}{216^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5^{3 (\frac{2}{3})}}{216^{\frac{2}{3}}}$

Rewrite the expression.

$\frac{5^{2}}{216^{\frac{2}{3}}}$

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

$\frac{25}{216^{\frac{2}{3}}}$

Simplify the denominator.

Rewrite $216$ as $6^{3}$ .

$\frac{25}{{(6^{3})}^{\frac{2}{3}}}$

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

$\frac{25}{6^{3 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{25}{6^{3 (\frac{2}{3})}}$

Rewrite the expression.

$\frac{25}{6^{2}}$

Raise $6$ to the power of $2$ .

$\frac{25}{36}$

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{36}$

Decimal Form:

$0.69\overline{4}$

Simplify (-216/125)^(-2/3)

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