Question

explain process
not answers
plis

Answer 1

Solution :-

$\implies\left[\left\{\left(-\dfrac{2}{5}\right)^2\right\}^{-2}\right]^{-1}$

Simplifying the innermost bracket by just squaring the terms.

$\implies\left[\left\{\left(-\dfrac{2}{5}\right)^2\right\}^{-2}\right]^{-1}$

$\implies\left[\left\{\dfrac{( - 2)^{2} }{ {5}^{2} }\right\}^{-2}\right]^{-1}$

$\implies\left[\left\{\dfrac{4 }{ 25 }\right\}^{-2}\right]^{-1}$

Simplifying the innermost bracket by squaring of reciprocal. negative power means power of reciprocal.

Inorder to make power positive, we just reciprocate the fraction.

$\implies\left[\left\{\dfrac{4 }{ 25 }\right\}^{-2}\right]^{-1}$

$\implies\left[\left\{\dfrac{25 }{4}\right\}^{2}\right]^{-1}$

$\implies\left[\dfrac{ {(25)}^{2} }{ {(4)}^{2} }\right]^{-1}$

$\implies\left[\dfrac{ 625 }{16}\right]^{-1}$

Again, the power is negative, so we just have to reciprocate the fraction to make power positive.

$\implies\left[\dfrac{ 625 }{16}\right]^{-1}$

$\implies\dfrac{16}{625}$

Therefore, the required answer is,

$\boxed{ \left[\left\{\left(-\dfrac{2}{5}\right)^2\right\}^{-2}\right]^{-1} = \dfrac{16}{625} }$