Question

The value of $(1024{)}^{-\frac{4}{5}}$ is ________.

• A. ${\left(\frac{1}{4}\right)}^3$
• B. ${\left(\frac{1}{4}\right)}^2$
• C. $\frac{1}{256}$
• D. $\frac{1}{512}$

Answer 1

Answer: (C)

$\frac{1}{256}$

$1024=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=2^{10}$

To find,

$(1024{)}^{-\frac{4}{5}}=2^{-\frac{10\times 4}{5}}$

$=2^{-8}$

$2^8=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=256$

$\therefore (1024{)}^{-\frac{4}{5}}=\frac{1}{256}$