Evaluate : $[[(- \frac {2}{3})^{-3}]^{-4}]^{-2}$

Given :

The given expression is  $[[(- \frac {2}{3})^{-3}]^{-4}]^{-2}$

To do :

We have to evaluate and find the value of the given expression.

Solution :

We know that,

$[a^m]^n = a^{m\times n}$

$[[(- \frac {2}{3})^{-3}]^{-4}]^{-2} =[(- \frac {2}{3})^{-3}]^{-4 \times -2}$

                          $ =[(- \frac {2}{3})^{-3}]^{8}$ 

                             $ =(- \frac {2}{3})^{-3\times 8}$ 

                               $ =(- \frac {2}{3})^{-24}$

This can be written as,

                         $ =(- \frac {3}{2})^{24}$

                          $= \frac{3^{24}}{2^{24}} = (\frac{3}{2})^{24}$   

The value of $[[(- \frac {2}{3})^{-3}]^{-4}]^{-2}$ is $(\frac{3}{2})^{24}$ 

Tutorialspoint

e

Updated on: 10-Oct-2022

44 Views

Kickstart Your Career

Get certified by completing the course

Get Started