Question

Simplify $[{\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{4}\right)}^{-2}]÷{\left(\frac{1}{5}\right)}^{-3}$

• A. $\frac{11}{125}$
• B. $125$
• C. $11$
• D. $\frac{-11}{125}$

Answer 1

The correct option is A $\frac{11}{125}$

$[{\left(\frac{1}{3}\right)}^{-3}-{\left(\frac{1}{4}\right)}^{-2}]÷{\left(\frac{1}{5}\right)}^{-3}$
$=[\frac{1^{-3}}{3^{-3}}-\frac{1^{-2}}{4^{-2}}]÷\frac{1^{-3}}{5^{-3}}$
$=(3^3-4^2)÷5^3$
$=(27-16)÷125$
$=11÷125$
$=\frac{11}{125}$

Hence, option $A$ is correct.