Question

Please give this answer if correct I will mark as brain list please it's urgent​

Answer 1

GIVEN :-

$\\ \red \bigstar \displaystyle \tt \: (7 ^{ - 1} - 8 ^{ - 1} ) ^{ - 1} - (3 ^{ - 1} - 4 ^{ - 1} ) ^{ - 1}$

TO FIND :-

$\\ \red \bigstar \displaystyle \tt \: value \: of \: \: (7 ^{ - 1} - 8 ^{ - 1} ) ^{ - 1} - (3 ^{ - 1} - 4 ^{ - 1} ) ^{ - 1}$

SOLUTION :-

$\\ : \implies \displaystyle \tt \: (7 ^{ - 1} - 8 ^{ - 1} ) ^{ - 1} - (3 ^{ - 1} - 4 ^{ - 1} ) ^{ - 1}$

$\orange\bigstar \red{ \tt By \ using \ identity :- a^{-1} = \dfrac{1}{a}}$

$\displaystyle \tt : \implies \Bigg \lgroup \bigg( \frac{1}{7} - \dfrac{1}{8} \bigg) ^{ - 1} \Bigg \rgroup - \Bigg \lgroup \bigg( \frac{1}{3} - \dfrac{1}{4} \bigg) ^{ - 1} \Bigg \rgroup$

$\displaystyle \tt : \implies \Bigg \lgroup \bigg( \frac{1 \times 8}{7 \times 8} - \dfrac{1 \times 7}{8 \times 7} \bigg) ^{ - 1} \Bigg \rgroup - \Bigg \lgroup \bigg( \frac{1 \times 4}{3 \times 4} - \dfrac{1 \times 3}{4 \times 3} \bigg) ^{ - 1} \Bigg \rgroup$

$\displaystyle \tt : \implies \Bigg \lgroup \bigg( \frac{8}{56} - \dfrac{7}{56} \bigg) ^{ - 1} \Bigg \rgroup - \Bigg \lgroup \bigg( \frac{4}{12} - \dfrac{3}{12} \bigg) ^{ - 1} \Bigg \rgroup$

$\displaystyle \tt : \implies \Bigg \lgroup \bigg( \frac{8 - 7}{56} \bigg) ^{ - 1} \Bigg \rgroup - \Bigg \lgroup \bigg( \frac{5 - 3}{12} \bigg) ^{ - 1} \Bigg \rgroup$

$\displaystyle \tt : \implies \Bigg \lgroup \bigg( \frac{1}{56} \bigg) ^{ - 1} \Bigg \rgroup - \Bigg \lgroup \bigg( \frac{1}{12} \bigg) ^{ - 1} \Bigg \rgroup$

$\displaystyle \tt : \implies \bigg( \frac{56}{1} \bigg) - \bigg( \frac{12}{1} \bigg)$

$\displaystyle \tt : \implies \dfrac{56 - 12}{1}$

$\red \bigstar \underline{\boxed{\displaystyle \tt \: (7 ^{ - 1} - 8 ^{ - 1} ) ^{ - 1} - (3 ^{ - 1} - 4 ^{ - 1} ) ^{ - 1} = 44 }}$

$\therefore \: \underline{ \displaystyle \tt The \: Required \: Answer \: is \: 44 }$

Option (1) ✅

Answer 2

Given Expression :-

(7-¹ – 8-¹)-¹ – (3-¹ – 4-¹)-¹

How To Solve?

Convert Negative Powers into positive and then Subtract them.

Solution :-

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

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

➝ $( { \dfrac{1}{56}) }^{ - 1} - { (\dfrac{1}{12} )}^{ - 1}$

➝ $\sf{56 - 12}$

➝ $\underline{\boxed{\bf\red{44}}}$

Hence, Correct Answer = 44.