If $ \frac{a}{b}=\left(\frac{3}{5}\right)^{18} \p\left(\frac{3}{5}\right)^{16}, $ find the value of $ \left(\frac{a}{b}\right)^{2} $

Given:

\( \frac{a}{b}=\left(\frac{3}{5}\right)^{18} \div\left(\frac{3}{5}\right)^{16} \).

To do:

We have to find the value of \( \left(\frac{a}{b}\right)^{2} \).

Solution:  

We know that,

$a^m \div a^n=a^{m-n}$

$a^m \times b^m=(a\times b)^m$

Therefore,

$\frac{a}{b}=(\frac{3}{5})^{18} \div (\frac{3}{5})^{16}$

$=(\frac{3}{5})^{18-16}$

$=(\frac{3}{5})^{2}$

$=\frac{9}{25}$

$(\frac{a}{b})^{2}=(\frac{9}{25})^{2}$

$=\frac{9^2}{25^2}$

$=\frac{81}{625}$

Therefore,

$(\frac{a}{b})^{2}=\frac{81}{625}$. 

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Updated on: 10-Oct-2022

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