Question

Find the value of ${\left(\frac{p}{q}\right)}^3$ if ${\left(\frac{7}{2}\right)}^{-4}\times {\left(\frac{4}{49}\right)}^3={\left(\frac{p}{q}\right)}^{-10}$

Answer 1

$(\frac{7}{2}{)}^{-4}\times (\frac{4}{49}{)}^3=(\frac{p}{q}{)}^{-10}$

This can be written as

$\Rightarrow \frac{7^{-4}}{2^{-4}}\times \frac{4^3}{{49}^3}=(\frac{p}{q}{)}^{-10}$

$\Rightarrow \frac{7^{-4}}{2^{-4}}\times \frac{2^6}{7^6}=(\frac{p}{q}{)}^{-10}$

$\Rightarrow \frac{7^{-4}}{2^{-4}}\times \frac{2^6}{7^6}=\frac{p^{-10}}{q^{-10}}$

$\Rightarrow \frac{7^{-10}}{2^{-10}}=\frac{p^{-10}}{q^{-10}}$

$\Rightarrow \frac{p}{q}=\frac{7}{2}$

$\Rightarrow (\frac{p}{q}{)}^3=(\frac{7}{2}{)}^3$

$\Rightarrow (\frac{p}{q}{)}^3=\frac{343}{8}$