Question

Simplify: $\left(\frac{1}{6^{(-2)}}-\frac{1}{3^{(-3)}}\right)÷\frac{1}{5^{(-2)}}$

• A. $\frac{5}{3}$
• B. $\frac{3}{5}$
• C. $\frac{9}{25}$
• D. $\frac{25}{9}$

Answer 1

The correct option is C

$\frac{9}{25}$

$(\frac{1}{6^{(-2)}}-\frac{1}{3^{(-3)}})÷\frac{1}{5^{(-2)}}$

$=\left(\right(6{)}^{-(-2)}-\left(3{)}^{-(-3)}\right)÷(5{)}^{-(-2)}$
$[\because \frac{1}{a^m}=(a{)}^{-m}]$

$=\left(\right(6{)}^2-\left(3{)}^3\right)÷(5{)}^2$

$=(36–27)÷\left(25\right)$

$=9\times \frac{1}{25}$

$=\frac{9}{25}$