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

Solution:

The correct option is (a)

Given, (7^-1 - 8^-1)^-1 - (3^-1 - 4^-1)^-1

Using laws of indices, For any non-zero integer a, a^m = 1/a^-m

7^-1 - 8^-1 = (1/7 - 1/ 8) = [(8 - 7)/56] = 1/56

∴ (7^-1 - 8^-1)^-1 = (1/56)^-1 = 56

3^-1 - 4^-1 = (1/3 - 1/4) = [(4 - 3)/12] = 1/12

∴ (3^-1 - 4^-1)^-1 = (1/12)^-1 = 12

Now (7^-1 - 8^-1)^-1 - (3^-1 - 4^-1)^-1 = 56 - 12 = 44

✦ Try This: The value of (8^-1 - 9^-1)^-1 - (10^-1 - 11^-1)^-1 is (a) 38, (b) 83, (c) -38, (d) -83

The correct option is (c)

Given, (8^-1 - 9^-1)^-1 - (10^-1 - 11^-1)^-1

using laws of indices, For any non-zero integer a, a^m = 1/a^-m

8^-1 - 9^-1 = (1/8 - 1/9) = [(9 - 8)/72] = 1/72

∴ (8^-1 - 9^-1)^-1 = (1/72)^-1 = 72

10^-1 - 11^-1 = (1/10 - 1/11) = [(11 - 10)/110] = 1/110

∴ (10^-1 - 11^-1)^-1 = (1/110)^-1 = 110

Now (8^-1 - 9^-1)^-1 - (10^-1 - 11^-1)^-1 = 72 - 110 = -38

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 23

The value of (7^-1 - 8^-1)^-1 - (3^-1 - 4^-1)-1 is (a) 44, (b) 56, (c) 68, (d) 12

Summary:

The value of (7^-1 - 8^-1)^-1 - (3^-1 - 4^-1)^-1 is 44

☛ Related Questions:

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