Question

The value of $[4^{-1}+3^{-1}+6^{-2}{]}^{-1}$ is ___.

• A. $\frac{36}{22}$
• B. $\frac{38}{22}$
• C. $\frac{36}{20}$
• D. $\frac{36}{11}$

Answer 1

The correct option is A

$\frac{36}{22}$

$Given,[4^{-1}+3^{-1}+6^{-2}{]}^{-1}$

= $(\frac{1}{4}+\frac{1}{3}+\frac{1}{36}{)}^{-1}$ ($\because \frac{1}{a^m}=(a{)}^{-m}$)

= $(\frac{9+12+1}{36}{)}^{-1}$

= $(\frac{22}{36}{)}^{-1}$

=$\frac{1}{\left(\frac{22}{36}\right)}$ ($\because (a{)}^{-m}=\frac{1}{a^m}$)

=$\frac{36}{22}$

$\therefore$The value of $[4^{-1}+3^{-1}+6^{-2}{]}^{-1}$ is $\frac{36}{22}$