Question

$\frac{\frac{2^2}{3^2}}{\frac{4^2}{5^2}}=$ ___

• A. $\frac{25}{64}$
• B. $\frac{64}{25}$
• C. $\frac{25}{36}$
• D. $\frac{36}{25}$

Answer 1

The correct option is C $\frac{25}{36}$

Using the law of exponents $\frac{a^m}{b^m}=(\frac{a}{b}{)}^m,$ we have
$\frac{\frac{2^2}{3^2}}{\frac{4^2}{5^2}}=\frac{{\left(\frac{2}{3}\right)}^2}{{\left(\frac{4}{5}\right)}^2}={\left(\frac{\frac{2}{3}}{\frac{4}{5}}\right)}^2$
$={\left(\frac{5}{6}\right)}^2$
$=\frac{25}{36}.$