# How do you solve fractional exponent with a fraction as a base (1/16)^(-3/4)?

Apr 14, 2015

color(blue)((1/a)^-m = a^m

${\left(\frac{1}{16}\right)}^{- \frac{3}{4}}$

$= {\left(16\right)}^{\frac{3}{4}}$

color(blue)(a^(m/n) = (a^(1/n))^m

$= {\left({16}^{\frac{1}{4}}\right)}^{3}$

$= {\left(\sqrt[4]{16}\right)}^{3}$

$= {\left(\sqrt[4]{{2}^{4}}\right)}^{3}$

$= {2}^{3}$

$= 8$

color(green)((1/16)^(-3/4) = 8