Question

simplify
${( - 4 \div 5)^{ - 2} } ^{ - 2}$
​

Answer 1

$\huge \blue { \frac{256}{625} }$

Step-by-step explanation:

$( - 4 \div 5) { {}^{ - 2} }^{ - 2} \\ \\ = > (\frac{ - 4}{5} ) { {}^{ - 2} }^{ - 2} \\ \\ = > ( \frac{ - 4}{5} {)}^{ - 2 \times - 2} \\ \\ = > ( \frac{ - 4}{5} {)}^{4} \\ \\ = > \frac{ - 4 \times - 4 \times - 4 \times - 4}{5 \times 5 \times 5 \times 5} \\ \\ = > \frac{256}{625}$

Hence the simplification is 256/625.

Things to remember :-

When bases are same (here x)

$({x}^{m} {)}^{n} = {x}^{m \times n} \\ {x}^{m} \times {x}^{n} = {x}^{m + n} \\ {x}^{m} \div {x}^{n} = {x}^{m - n}$

using identity (1) we solved this question.

hope it helps.

Answer 2

$\large \bold \color{blue}{Explanation}$

$\implies$ $\large\frac({-4}{5})^{-2}^{-2}$

$\implies$ $\large\cfrac({-4}{5})^{(4)}$

$\implies$ $\large\cfrac{256}{625}$

Hope it helps you!