(7/9)^2 ÷(14/3)^2

Given:

$(\frac{7}{9})^2 ÷(\frac{14}{3})^2$

To do:

 We have to find the value of $(\frac{7}{9})^2 ÷(\frac{14}{3})^2$.

Solution:

We know that,

$\frac{a^m}{b^m}=(\frac{a}{b})^m$

$\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$

Therefore,

$(\frac{7}{9})^2 ÷(\frac{14}{3})^2=(\frac{7}{9}\div \frac{14}{3})^2$

$=(\frac{7}{9}\times\frac{3}{14})^2$

$=(\frac{1\times1}{3\times2})^2$

$=(\frac{1}{6})^2$

$=\frac{1^2}{6^2}$

$=\frac{1}{36}$

Therefore, $(\frac{7}{9})^2 ÷(\frac{14}{3})^2=\frac{1}{36}$.

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Updated on: 10-Oct-2022

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