How do you simplify 256^(-7/8)?

Apr 8, 2015

color(red)(256^(-7/8)

$= {\left({\left(256\right)}^{\frac{1}{8}}\right)}^{-} 7$

$= {\left(\sqrt[8]{256}\right)}^{-} 7$

$= {\left(2\right)}^{-} 7$

$= \frac{1}{{2}^{7}}$

color(green)( = 1/ 128