Question

Which one of the following options is the same as $[5^{-1}+{10}^{-1}+2^{-2}{]}^{-1}$?

• A. $\frac{11}{20}$
• B. $\frac{20}{11}$
• C. $\frac{4}{5}$
• D. $\frac{5}{4}$

Answer 1

The correct option is B $\frac{20}{11}$

Using the law of exponents, for a non-zero integer $a$ and an integer $m$, we have
$a^{-m}=\frac{1}{a^m}.$
$\therefore [5^{-1}+{10}^{-1}+2^{-2}{]}^{-1}={(\frac{1}{5}+\frac{1}{10}+\frac{1}{2^2})}^{-1}={\left(\frac{4+2+5}{20}\right)}^{-1}={\left(\frac{11}{20}\right)}^{-1}$
Now, $(\frac{11}{20}{)}^{-1}=\frac{1}{\frac{11}{20}}=\frac{20}{11}.$
Hence, $[5^{-1}+{10}^{-1}+2^{-2}{]}^{-1}=\frac{20}{11}.$