Page 108 - Maths Skills - 7

106 Maths

(iii) 243 = 3 × 3 × 3 × 3 × 3 = 3 (iv) 1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 = 2 × 3 = (2 × 3) = 6 4
4
4
4
5
3 243 2 1296
3 81 2 648
3 27 2 324
3 9 2 162

3 3 3 81
1 3 27
3 9
3 3

1

Example 5: Express each of the following as product of exponents.
(i) 648 (ii) 3600

Solution: (i) 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3 = 2 × 3 4 (ii) 3600 = 2 × 2 × 2 × 2 × 3× 3 × 5 × 5
3
2 648 = 2 × 3 × 5 2 2 3600
2
4
2 324 2 1800
2 162 2 900
3 81 2 450
3 27 3 225

3 9 3 75
3 3 5 25

1 5 5
1
Example 6: Simplify.
(i) 7 × 2 (ii) 2 × 5 (iii) 3 × 4 (iv) 3 × 10 4
2
3
4
2
2
Solution: (i) 7 × 2 = 7 × 7 × 2 × 2 (ii) 2 × 5 = 2 × 2 × 2 × 5
3
2
2
= 49 × 4 = 196 = 8 × 5 = 40
(iii) 3 × 4 = 3 × 4 × 4 × 4 × 4 (iv) 3 × 10 = 3 × 3 × 10 × 10 × 10 × 10
4
4
2
= 3 × 256 = 768 = 9 × 10000 = 90000
Example 7: Find the value of x, when
(i) 5 = 625 (ii) –3 = –243
x
x
Solution: (i) 5 = 625 (ii) –3 = –243
x
x
5 = 5 × 5 × 5 × 5 = 5 4 or 3 = 243
x
x
Then, x = 4 or 3 = 3 × 3 × 3 × 3 × 3
x
or 3 = 3 5 3 243
x
5 625 x = 5 3 81
5 125 3 27
5 25 3 9
5 5 3 3
1 1