Question

Simplify : $(6^{-1}-8^{-1}{)}^{-1}+(2^{-1}-3^{-1}{)}^{-1}$ is-

• A. $20$
• B. $30$
• C. $10$
• D. $40$

Answer 1

The correct option is B $30$

Law of exponents,

Given - $(6^{-1}-8^{-1}{)}^{-1}+(2^{-1}-3^{-1}{)}^{-1}$

$={(\frac{1}{6}-\frac{1}{8})}^{-1}+{(\frac{1}{2}-\frac{1}{3})}^{-1}$

$={\left(\frac{8-6}{6\times 8}\right)}^{-1}+{\left(\frac{3-2}{2\times 3}\right)}^{-1}$

$={\left(\frac{2}{36\times 8}\right)}^{-1}+{\left(\frac{1}{2\times 3}\right)}^{-1}$

$={\left(\frac{1}{24}\right)}^{-1}+{\left(\frac{1}{6}\right)}^{-1}$

$=24+6$

$=30$

Hence, option B is correct.