EXPONENTS AND POWERS 253- Express each of the following numbers using exponential notation:
(i) 5 1 2 (ii) 3 4 3 (iii) 7 2 9 (iv) 3125 - Identify the greater number, wherever possible, in each of the following?
(i) 4^3 or 3^4 (ii) 5^3 or 3^5 (iii) 2^8 or 8^2
(iv) 100^2 or 2^100 (v) 2^10 or 10^2 - Express each of the following as product of powers of their prime factors:
(i) 6 4 8 (ii) 4 0 5 (iii) 5 4 0 (iv) 3,600 - Simplify :
(i) 2 × 10^3 (ii) 7^2 × 2^2 (iii) 2^3 × 5 (iv) 3 × 4^4
(v) 0 × 10^2 (vi) 5^2 × 3^3 (vii) 2^4 × 3^2 (viii) 3^2 × 10^4 - Simplify :
(i) (– 4)^3 (ii) (–3) × (–2)^3 (iii) (–3)^2 × (–5)^2
(iv) (–2)^3 × (–10)^3 - Compare the following numbers:
(i) 2.7 × 10^12 ; 1.5 × 10^8 (ii) 4 × 10^14 ; 3 × 10^17
13.3 LAWS OF EXPONENTS
13.3.1 Multiplying Powers with the Same Base
(i) Let us calculate 2^2 × 2^3
22 × 2^3 = (2 × 2) × (2 × 2 × 2)
= 2 × 2 × 2 × 2 × 2 = 2^5 = 22+3
Note that the base in 2^2 and 2^3 is same and the sum of the exponents, i.e., 2 and 3 is 5
(ii) (–3)^4 × (–3)^3 = [(–3) × (–3) × (–3)× (–3)] × [(–3) × (–3) × (–3)]
= (–3) × (–3) × (–3) × (–3) × (–3) × (–3) × (–3)
= (–3)^7
= (–3)4+3
Again, note that the base is same and the sum of exponents, i.e., 4 and 3, is 7
(iii) a^2 × a^4 = (a×a) × (a×a×a×a)
=a×a × a×a × a×a = a^6
(Note: the base is the same and the sum of the exponents is 2 + 4 = 6)
Similarly, verify :
42 × 4^2 =42+2
32 × 3^3 =32+3