Simplify (-243/8)^(-2/5)

${(- \frac{243}{8})}^{- \frac{2}{5}}$

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

${(- \frac{8}{243})}^{\frac{2}{5}}$

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

Apply the product rule to $- \frac{8}{243}$ .

${(- 1)}^{\frac{2}{5}} {(\frac{8}{243})}^{\frac{2}{5}}$

Apply the product rule to $\frac{8}{243}$ .

${(- 1)}^{\frac{2}{5}} \frac{8^{\frac{2}{5}}}{243^{\frac{2}{5}}}$

Reduce the expression by cancelling the common factors.

Rewrite $- 1$ as ${(- 1)}^{5}$ .

${({(- 1)}^{5})}^{\frac{2}{5}} \frac{8^{\frac{2}{5}}}{243^{\frac{2}{5}}}$

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

${(- 1)}^{5 (\frac{2}{5})} \frac{8^{\frac{2}{5}}}{243^{\frac{2}{5}}}$

Cancel the common factor of $5$ .

Cancel the common factor.

${(- 1)}^{5 (\frac{2}{5})} \frac{8^{\frac{2}{5}}}{243^{\frac{2}{5}}}$

Rewrite the expression.

${(- 1)}^{2} \frac{8^{\frac{2}{5}}}{243^{\frac{2}{5}}}$

Simplify the expression.

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

$1 \frac{8^{\frac{2}{5}}}{243^{\frac{2}{5}}}$

Multiply $\frac{8^{\frac{2}{5}}}{243^{\frac{2}{5}}}$ by $1$ .

$\frac{8^{\frac{2}{5}}}{243^{\frac{2}{5}}}$

Simplify the denominator.

Rewrite $243$ as $3^{5}$ .

$\frac{8^{\frac{2}{5}}}{{(3^{5})}^{\frac{2}{5}}}$

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

$\frac{8^{\frac{2}{5}}}{3^{5 (\frac{2}{5})}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{8^{\frac{2}{5}}}{3^{5 (\frac{2}{5})}}$

Rewrite the expression.

$\frac{8^{\frac{2}{5}}}{3^{2}}$

Raise $3$ to the power of $2$ .

$\frac{8^{\frac{2}{5}}}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{8^{\frac{2}{5}}}{9}$

Decimal Form:

$0.25526630 \dots$