Page 89 - Start Up Mathematics_7

8
8
8
8
2 × a 5 2 × a 5 2 × a 5 2 × a 5
2
2
(g) = = = = 2 8 – 6 × a 5 – 3 = 2 × a = (2a) 2
3
2 3
6
4 × a 3 (2 ) × a 3 2 × × a 3 2 × a 3
5
8 3
7 × a b
3
3
0
(h) = 7 5 – 5 × a 8 – 5 × b 3 – 2 = 7 × a × b = a b
5 2
5
7 × a b
Example 11: State true or false after giving proper justification:
2
3
3
9
9
5
0
5
(a) 10 × 10 = 100 (b) 3 > 5 (c) 2 × 5 = 10 (d) 4 = (1,000) 0
9
Solution: (a) 10 × 10 = 100 9
9
LHS = 10 × 10 = 10 1 + 9 = 10 10 Quiz
9
2 9
RHS = 100 = (10 ) = 10 2 × 9 = 10 18 Which is greater?
9
9
 10 × 10 ≠ 100 , ∴ the statement is false 32 or 4 100
50
5
(b) 3 > 5 3
⇔ 243 > 125, which is correct, ∴ the statement is true
3
2
(c) 2 × 5 = 10 5
3
2
LHS = 2 × 5 = 8 × 25 = 200
5
RHS = 10 = 1,00,000
 200 ≠ 1,00,000, ∴ the statement is false
0
(d) 4 = (1,000) 0
⇔ 1 = 1 ( any non-zero real number raised to the power zero is 1.)
∴ the statement is true
Example 12: Express each of the following as a product of their prime factors only in exponential
form:
(a) 72 × 192 (b) 380 (c) 1,536
Solution: (a) 72 × 192 = (2 × 2 × 2 × 3 × 3) × (2 × 2 × 2 × 2 × 2 × 2 × 3)
3
1
6
9
2
= (2 × 3 ) × (2 × 3 ) = 2 3 + 6 × 3 2 + 1 = 2 × 3 3
2
(b) 380 = 38 × 10 = (19 × 2) × (2 × 5) = 19 × 2 × 5
9
(c) 1,536 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 2 × 3
Example 13: Simplify:
15
2
3 11 ( )3 4 2 × 5 × 5 - 6 25 × 5 × t 9
(a) (b) (c)
3
8
9
3 × 3 6 5 × ( )3 2 4 10 × t 3
3 11 3 11 3 11 1 1
–3
Solution: (a) = = = 3 11 – 14 = 3 = =
8
3 × 3 6 3 8 + 6 3 14 3 3 27
15
( )3 4 2 × 5 × 5 - 6 3 4 × 2 × 5 15 – 6 3 × 5 9
8
0
0
(b) = = = 3 8 – 8 × 5 9 – 9 = 3 × 5 = 1
9
2 4
9
3
9
5 × ( ) 5 × 3 2 × 4 5 × 3 8
2
2
2
25 × 5 × t 9 5 × 5 × t 9 5 2 + 2 × t 9 5 4 – 3 × t 9 – 3 5 × t 6 5t 6
(c) 3 3 = 3 3 = = = =
10 × t (2 × 5) × t 2 × 5 3 × 3 2 3 8 8
3
t
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