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