Question

Question 23

In the following question, out of the four options, only one is correct. Write the correct answer:

The value of$(7^{-1}-8^{-1}{)}^{-1}-(3^{-1}-4^{-1}{)}^{-1}$:
(a) 44
(b) 56
(c) 68
(d) 12

Answer 1

Using the law of exponents,
$a^{-m}=\frac{1}{a^m}$

$\therefore (7^{-1}-8^{-1}{)}^{-1}-(3^{-1}-4^{-1}{)}^{-1}$

$={(\frac{1}{7}-\frac{1}{8})}^{-1}-{(\frac{1}{3}-\frac{1}{4})}^{-1}$

$={\left(\frac{1}{56}\right)}^{-1}-{\left(\frac{1}{12}\right)}^{-1}$

$=56-12$
$=44$