Question

Question 6
Simplify $(256{)}^{-\left(4^{-\frac{3}{2}}\right)}$

Answer 1

$(256{)}^{-\left(4^{-\frac{3}{2}}\right)}=(256{)}^{-(4{)}^{-\frac{3}{2}}}=(256{)}^{-(2^2{)}^{-\frac{3}{2}}}$
$=(256{)}^{-\left(2^{2\times -\frac{3}{2}}\right)}=(256{)}^{-\left(2^{-3}\right)}[\because b^{(a^m{)}^n}=b^{a^{mn}}]$
$=(2^8{)}^{-\left(\frac{1}{2^3}\right)}=(2^8{)}^{-}\frac{1}{8}$
$=2^{8\times -\frac{1}{8}}=2^{-1}=\frac{1}{2}$