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Step-by-step explanation:
Given :-
[(7^-1-9^-1)^-1] +[(3^-1+5^-1)^-1]
To find :-
Solve the expression ?
Solution :-
Given expression is [(7^-1-9^-1)^-1] +[(3^-1+5^-1)^-1]
We know that a^-n = 1/a^n
=> [(1/7)-(1/9)]^-1 + [(1/3)+(1/5)]^-1
LCM of 7 and 9 = 63
LCM of 3 and 5 = 15
=> [(9-7)/63]^-1 + [(5+3)/15]^-1
=> (2/63)^-1 + (8/15)^-1
We know that a^-n = 1/a^n
=> [1/(2/63)]+[1/(8/15)]
=> (63/2)+(15/8)
LCM of 2 and 8 = 8
=> [(63×4)+(15×1)]/8
=> (252+15)/8
=> 267/8
Answer:-
The value of [(7^-1-9^-1)^-1] +[(3^-1+5^-1)^-1] is 267/8
Used formulae:-
→ a^-n = 1/a^n
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