Question
When simplified $\big(256\big)^{-\Big((4^{-\frac{3}{2}}\Big)}$ is:
- $8$
- $\frac{1}{8}$
- $2$
- $\frac{1}{2}$
✓
Answer
- $\frac{1}{2}$
Simplify $\big(256\big)^{-\Big((4^{-\frac{3}{2}}\Big)}$
$\big(256\big)^{-\Big((4^{-\frac{3}{2}}\Big)}=\big(256\big)^{-(2^2)^{-\frac{3}{2}}}$
$=\big(256\big)^{\Big(2^{2\times-\frac{3}{2}}\Big)}$
$\big(256\big)^{-\Big((4^{-\frac{3}{2}}\Big)}=\big(256\big)^{-(2)^{(-3)}}$
$\big(256\big)^{\Big(-4^{-\frac{3}{2}}\Big)}=\big(256\big)^{\frac{1}{(-2) ^3}}$
$=\big(256\big)^{\frac{1}{-8}}$
$=\big(2^8\big)^{\frac{1}{-8}}$
$=2^{8\times\frac{1}{-8}}$
$\big(256\big)^{-\Big((4^{-\frac{3}{2}}\Big)}=2^{8\times\frac{1}{-8}}=\frac{1}{2}$
Hence the correct choice is d.
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