Question

If ${\left(\frac{5}{9}\right)}^{-4}\times {\left(\frac{7}{5}\right)}^{-4}=\left(\frac{p}{q}\right)$, find ${\left(\frac{p}{q}\right)}^{-2}$

Answer 1

Given,

$(\frac{5}{9}{)}^{-}4\times (\frac{7}{5}{)}^{-}4=\left(\frac{p}{q}\right)$

$=>(\frac{7}{9}{)}^{-}4=(\frac{p}{q})$

$=>\frac{p}{q}=(\frac{9}{5}{)}^4$

Now,

$(\frac{p}{q}{)}^{-}2=((\frac{9}{7}{)}^4{)}^{-}2$

$=>(\frac{9}{7}{)}^2$

$=>\frac{81}{49}$