ML Aggarwal CBSE Solutions Class 8 Math Second Chapter Exponents and Powers Exercise 2.1

(1) (i) (3/5)^-2 = 1/(3/5)² = (5/3)²

= 5×5/3×3 = 25/9

(ii) (-3)^-3 = 1/(-3)³ = (1/-3)³ = 1x1x1/-3x-3x-3 = 1/-27

(2) (i) [(2)^-1+ (4)^-1+ (3)^-1]^-1

= [1/2 + 1/4 + 1/3]^-1 = [6+3+4/12]^-1 = [13/12]^-1

= 1/(13/12)¹ = 12/13 Ans.

(iii) [4⁰+4²-2³] x3^-2

= [1+16-8] x 1/32 = [17-8] x 1/3² = 9×1/9

= 1 Ans.

(4) (i) 16^-2 = 1/16² = 1/(2⁴)² = ½⁸ = 2^-8

(ii) 125^-4 = 1/(125)⁴ = 1/(5³)⁴ = 1/5¹² = 5^-12

(5) (ii) 3007.805

= 3×1000 + 0x100 + 0x10 + 7×1 + 8/10 + 0/100 + 5/1000

= 3×10^-3 + 0x10^-2 + 0x10^-1 + 7×1 + 8×10^-1 + 0x10^-2 x 5×10^-3

(9) 9^m ÷ 3^-2 = 9⁴

= 9^m ÷ 3^-2 = 9⁴

Or, 9^m ÷ 1/3² = 9⁴

Or, 9^m x 3² = 9⁴

Or, 9^m/9⁴ = 1/9

Or, (9)^m-4 = 1/9 = 9^-1

Or, m-4 = -1

Therefore, m= -1+4 = 3 Ans.

(11) Let, the number should be divided by X.

Therefore, according to question –

(3/-2)^-3 ÷ X = (2/3)²

Or, (3/-2)²/X = (2/3)²

Or, X = (3/-2)^-3/(2/3)²

Or, X = (-2/3)³/(2/3)² = – (2/3)^3-2 = – 2/3 Ans.

(12) (-2/3)^-13x (3/-2)⁸ = (-2/3)^-2X+1

Or, (-2/3)^-13 x (-2/3)^-8 = (-2/3)^-2X+1

Or, (-2/3)^-13-(-8)= (-2/3)^-2X+1

Or, (-2/3)^-13+8= (-2/3)^-2X+1

Or, (-2/3)^-5 = (-2/3)^-2X+1

Or, -2X+1 = -5

Or, -2X = -5-1 = -6

Or, X = 6/2 = 3 Ans.