Simplify:$\left[\left(\frac{-2}{5}\right)^{3}\right]^{4}$

Given: $\left[\left(\frac{-2}{5}\right)^{3}\right]^{4}$.

To find: Here we have to find the value of the given expression $\left[\left(\frac{-2}{5}\right)^{3}\right]^{4}$.

Solution:

$\left[\left(\frac{-2}{5}\right)^{3}\right]^{4}$

$=\ \left[\frac{-2\ \times \ -2\ \times \ -2}{5\ \times \ 5\ \times \ 5}\right]^{4}$

$=\ \left[\frac{-8}{125}\right]^{4}$

$=\ \frac{-8\ \times \ -8\ \times \ -8\ \times \ -8}{125\ \times \ 125\ \times \ 125\ \times \ 125}$

$=\ \mathbf{\frac{4096}{244140625}}$

So, value of the given expression is $\frac{4096}{244140625}$.