Question

Evaluate :- ${\left(\frac{2}{7}\right)}^2\times {\left(\frac{7}{2}\right)}^{-3}÷{\left\{{\left(\frac{7}{5}\right)}^{-2}\right\}}^{-4}$

Answer 1

Consider the given integral.

$={\left(\frac{2}{7}\right)}^2\times {\left(\frac{7}{2}\right)}^{-3}÷{\left\{{\left(\frac{7}{5}\right)}^{-2}\right\}}^{-4}$

$={\left(\frac{2}{7}\right)}^2\times {\left(\frac{2}{7}\right)}^3÷{\left(\frac{7}{5}\right)}^8$

$=\frac{{\left(\frac{2}{7}\right)}^5}{{\left(\frac{7}{5}\right)}^8}$

$=\frac{2^5\times 5^8}{7^5\times 7^8}$

$=\frac{2^5\times 5^8}{7^{13}}$

Hence, the value of this expression is $\frac{2^5\times 5^8}{7^{13}}$.