Question

Question 44

In the following question, fill in the blanks to make the statements true.

$[4^{-1}+3^{-1}+6^{-2}{]}^{-1}=$___

Answer 1

Using law of exponents,
$a^{-m}=\frac{1}{a^m}$
$\therefore [4^{-1}+3^{-1}+6^{-2}{]}^{-1}={(\frac{1}{4}+\frac{1}{3}+\frac{1}{36})}^{-1}={\left(\frac{9+12+1}{36}\right)}^{-1}={\left(\frac{22}{36}\right)}^{-1}=\frac{36}{22}=\frac{18}{11}$

Hence ,
$[4^{-1}+3^{-1}+6^{-2}{]}^{-1}=\frac{18}{11}$