Question

Evaluate the expression: ${\left(\frac{5}{3}\right)}^{-6}\times {\left(\frac{3^2}{5^2}\right)}^{-2}$

• A. $\frac{25}{9}$
• B. $-\frac{25}{9}$
• C. $\frac{9}{25}$
• D. $-\frac{9}{25}$

Answer 1

The correct option is C $\frac{9}{25}$

${\left(\frac{5}{3}\right)}^{-6}\times {\left(\frac{3^2}{5^2}\right)}^{-2}$
=$\frac{5^{-6}}{3^{-6}}\times \frac{3^{-4}}{5^{-4}}=\frac{5^{-2}}{3^{-2}}$
$=\frac{3^2}{5^2}$
$=\frac{9}{25}$

Hence, option $C$ is correct.