Page 73 - ICSE Math 7

0
0
0
(f) (3 + 2 ) × 5 = (1 + 1) × 1 = 2 = 2 1
8
8
5
8
5
8
5
2 × a 2 × a 2 × a 5 2 × a
(g) = = = = 2 8 – 6 × a 5 – 3 = 2 × a = (2a) 2
2
2
6
3
2 3
4 × a 3 (2 ) × a 3 2 × × a 3 2 × a 3
5
8 3
7 × a b
3
0
3
(h) = 7 5 – 5 × a 8 – 5 × b 3 – 2 = 7 × a × b = a b
5 2
5
7 × a b
Example 10: 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)
1
3
9
6
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 11: Simplify.
15
2
9
3 11 ( )3 4 2 × 5 × 5 - 6 25 × 5 × t
(a) (b) (c)
8
3
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
5 × ( )3 2 4 5 × 3 2 × 4 5 × 3 8
9
9
4
2
2
2
25 × 5 × t 9 5 × 5 × t 9 5 2 + 2 × t 9 5 × t 9 5 4 – 3 × t 9 – 3
(c) = = = =
3
3
3
3
3
3
10 × t 3 (2 × 5) × t 3 2 × 5 × t 3 2 × 5 × t 3 2 3
5 × t 6 5t 6
= =
8 8
Example 12: Simplify.
3 2
3 4
2 2 3
2
4 2 6 2
(a) (4x yz ) – (2x y z ) (b) (4ab ) ÷ (8a b )
 1 − 3   5  2 4    − 3  2 125 
2 0
–6
–4
(c) (3 ) + 3 ÷ 3 +   (d)    ×  ÷    × 
 3    8  5     5  81 


m
3 4
2
m
m
4
2
3 4
Solution: (a) (4x yz ) = 4 × (x yz ) [Using (ab) = a × b ]
3 4
2 4 4
= 256 (x ) y (z )
m n
8 4 12
= 256x y z [Using (a ) = a m×n ]
4 2 6 2
m
m
2
4 2 6 2
m
(2x y z ) = 2 × (x y z ) [Using (ab) = a × b ]
2 2
4 2
6 2
= 4(x ) (y ) (z )
m n
8 4 12
= 4x y z [Using (a ) = a m×n ]
8 4 12
2
3 4
8 4 12
4 2 6 2
\ (4x yz ) – (2x y z ) = 256x y z – 4x y z
8 4 12
8 4 12
= (256 – 4) x y z = 252 x y z
3 2
(4ab )
3 2
2 2 3
(b) (4ab ) ÷ (8a b ) =
2 2 3
(8a b )
2
3 2
4 × (ab )
m
m
m
= [Using (ab) = a × b ]
2 2 3
3
8 × (a b )
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