308 MATHEMATICS- (i) False; 10 × 10^11 = 10^12 and (100)^11 = 10^22 (ii) False; 2^3 = 8, 5^2 = 25
(iii) False; 6^5 = 2^5 × 3^5 (iv) True; 3^0 = 1, (1000)^0 = 1 - (i) 28 × 3^4 (ii) 2 × 3^3 × 5 (iii) 3^6 × 2^6 (iv) 2^8 × 3 5. (i) 98 (ii)
5t^4
8 (iii) 1
EXERCISE 13.3 - 279404 = 2 × 10^5 + 7 × 10^4 + 9 × 10^3 + 4 × 10^2 + 0 × 10^1 + 4 × 10^0
3006194 = 3 × 10^6 + 0 × 10^5 + 0 × 10^4 + 6 × 10^3 + 1 × 10^2 + 9 × 10^1 + 4 × 10^0
2806196 = 2 × 10^6 + 8 × 10^5 + 0 × 10^4 + 6 × 10^3 + 1 × 10^2 + 9 × 10^1 + 6 × 10^0
120719 = 1 × 10^5 + 2 × 10^4 + 0 × 10^3 + 7 × 10^2 + 1 × 10^1 + 9 × 10^0
20068 = 2 × 10^4 + 0 × 10^3 + 0 × 10^2 + 6 × 10^1 + 8 × 10^0 - (a) 86045 (b) 405302 (c) 30705 (d) 900230
- (i) 5 × 10^7 (ii) 7 × 10^6 (iii) 3.1865 × 10^9 (iv) 3.90878 × 10^5
(v) 3.90878 × 10^4 (vi) 3.90878 × 10^3 - (a) 3.84 × 10^8 m (b) 3 × 10^8 m/s (c) 1.2756 × 10^7 m (d) 1.4 × 10^9 m
(e) 1 × 10^11 (f) 1.2 × 10^10 years (g) 3 × 10^20 m (h) 6.023 × 10^22
(i) 1.353 × 10^9 km^3 (j) 1.027 × 10^9
EXERCISE 14.1
(a) (b) (c)(d) (e) (f)