Write each of the following in exponential form:

Question:

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) $\left(\frac{2}{5}\right)^{-2} \times\left(\frac{2}{5}\right)^{-2} \times\left(\frac{2}{5}\right)^{-2}$

Solution:

(i) $\left(\frac{3}{2}\right)^{-1} \times\left(\frac{3}{2}\right)^{-1} \times\left(\frac{3}{2}\right)^{-1} \times\left(\frac{3}{2}\right)^{-1}=\left(\frac{3}{2}\right)^{-1+(-1)+(-1)+(-1)}$                  $\left\{a^{m} \times a^{n}=a^{m+n}\right\}$

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

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

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

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

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