Evaluate-
i. {(1/3)^-1 - (1/4)^-1)}^-1
ii. (5/8)^-7 × (8/5)^-4

The correct answer is: Answers to the given equations are:- -1 & 512 / 125 = 4.096 respectively.

Step-by-step solution:-
i. {(1/3)^-1 - (1/4)^-1)}^-1
= 1 / {(3/1)¹ - (4/1)¹}¹ …................................................. (b^-n = 1 / bⁿ)
= 1 / {3 - 4} .................................................................... (b¹ = b)
= 1 / -1
= -1
ii. (5/8)^-7 × (8/5)^-4
= (8/5)⁷ × (5/8)⁴ ............................................................ (b^-n = 1 / bⁿ)
= 8⁷ / 5⁷ × 5⁴ / 8⁴ .......................................................... [aⁿ/bⁿ = (a/b)ⁿ]
= 8⁷ × 5⁴ / 5⁷ × 8⁴
= 8^7-4 / 5^7-4 .................................................................... (aⁿ/a^m = a^n-m)
= 8³ / 5³
= 512 / 125
Final Answer:-
∴ Answers to the given equations are:- -1 & 512 / 125 = 4.096 respectively.