Write each of the following in exponential form:(i) $ \left(\frac{3}{2}\right)^{-1} \times\left(\frac{3}{2}\right)^{-1} \times\left(\frac{3}{2}\right)^{-1} \times\left(\frac{3}{2}\right)^{-1} $
(ii) $ \left(\frac{2}{5}\right)^{-2} \times\left(\frac{2}{5}\right)^{-2} \times\left(\frac{2}{5}\right)^{-2} $

To do:  

We have to write given expressions in exponential form.

Solution:

We know that,

$a^m \times a^n =a^{m+n}$

$a^{-m}=\frac{1}{a^m}$

Therefore,

(i) $(\frac{3}{2})^{-1} \times(\frac{3}{2})^{-1} \times(\frac{3}{2})^{-1} \times(\frac{3}{2})^{-1}=(\frac{3}{2})^{(-1)+(-1)+(-1)+(-1)}$

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

$=(\frac{2}{3})^4$

(ii) $(\frac{2}{5})^{-2} \times(\frac{2}{5})^{-2} \times(\frac{2}{5})^{-2}=(\frac{2}{5})^{(-2)+(-2)+(-2)}$

$=(\frac{2}{5})^{-6}$

$=(\frac{5}{2})^6$

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Updated on: 10-Oct-2022

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