Question:
Simplify (256) $-\left(4^{-\frac{3}{2}}\right)$
Solution:
$(256)^{-\left(4^{-\frac{3}{2}}\right)}=(256)^{-(4)^{-\frac{3}{2}}}=(256)^{-\left(2^{2}\right)^{-\frac{3}{2}}} .$
$=(256)^{-\left(2^{2 x-\frac{3}{2}}\right)}=(256)^{-\left(2^{-3}\right)}$ $\left[\because b^{\left(a^{m}\right)^{n}}=b^{a^{m n}}\right]$
$=\left(2^{8}\right)^{-\left(\frac{1}{2^{3}}\right)}=\left(2^{8}\right)^{-\frac{1}{8}}$
$=2^{8 x-\frac{1}{8}}=2^{-1}=\frac{1}{2}$
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