Evaluate
(i) {(1/3)⁻¹ − (1/4)⁻¹}⁻¹    (ii) (5/8)⁻⁷× (8/5)⁻⁴

Solution:

(i) {(1/3)⁻¹ − (1/4)⁻¹}⁻¹ 

According to the rules of exponents,

(a/b)^−m = (b/a)^m

{(1/3)⁻¹ − (1/4)⁻¹}⁻¹

= (3¹ − 4¹)⁻¹

= (3 − 4)⁻¹

= (−1)⁻¹

= (−1/1)¹= −1

(ii) (5/8)⁻⁷× (8/5)⁻⁴ 

According to the rules of exponents,

We know that, (a/b)^−m = (b/a)^m

(5/8)⁻⁷× (8/5)⁻⁴

= (8/5)⁷ × (8/5)⁻⁴

= (8/5)³  [Since, a^m/aⁿ = a^{m - n}]

= 512/125

☛ Check: NCERT Solutions for Class 8 Maths Chapter 12

Video Solution:

Evaluate (i) {(1/3)⁻¹ − (1/4)⁻¹}⁻¹    (ii) (5/8)⁻⁷× (8/5)⁻⁴

Class 8 Maths NCERT Solutions Chapter 12 Exercise 12.1 Question 6

Summary:

The value of the following expressions are (i) {(1/3)⁻¹ − (1/4)⁻¹}^-1 = -1   (ii) (5/8)⁻⁷× (8/5)⁻⁴ = 512/125

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