# How do you simplify 1/32 to the power of -3/5?

Apr 14, 2015

Note that:
${2}^{5} = 32$

${b}^{- a} = \frac{1}{{b}^{a}}$

and
${b}^{\frac{p}{q}} = {\left(\sqrt[q]{b}\right)}^{p}$

Therefore
$\frac{1}{32} ^ \left(- \frac{3}{5}\right)$

$= {32}^{\frac{3}{5}}$

$= {\left(\sqrt[5]{32}\right)}^{3}$

$= {2}^{3}$

$= 8$