**ML Aggarwal CBSE Solutions Class 8 Math 2nd 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) **[4^{0}+4^{2}-2^{3}] x3^{-2}

= [1+16-8] x 1/32 = [17-8] x 1/3^{2} = 9×1/9

= 1 Ans.

**(4) (i)** 16^{-2} = 1/16^{2} = 1/(2^{4})^{2} = ½^{8} = 2^{-8}

(ii) 125^{-4} = 1/(125)^{4} = 1/(5^{3})^{4} = 1/5^{12} = 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} = 9^{4}

= 9^{m} ÷ 3^{-2} = 9^{4}

Or, 9^{m} ÷ 1/3^{2} = 9^{4}

Or, 9^{m} x 3^{2} = 9^{4}

Or, 9^{m}/9^{4} = 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)^{-13 }x (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.