Question

(256)^-3/4
express the answer as a rational number in its standard form ​

Answer 1

Answer:

${256} \\ = 16 \times 16 \\ = 4 \times 4 \times 4 \times 4 \\ = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$

Therefore,

$256 = {2}^{8}$

${256}^{ \frac{ - 3}{4} } = {2}^{ \frac{8 \times - 3}{4} } = {2}^{ - 6}$

$= { \frac{1}{2} }^{6} \\ = \frac{1}{64}$

THEREFORE,

Answer :-

$\frac{1}{64}$