Page 111 - Maths Skills - 7

Exponents and Powers 109

Example 3: Simplify the following:
(i) (4 + 2 ) × 6 (ii) 3 × 4 × 5 (iii) (1 + 2 + 3 ) × 7 (iv) (8 ÷ 6 ) – (4 ÷ 3 )
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Solution: (i) (4 + 2 ) × 6 [a = 1] (ii) 3 × 4 × 5 = 1 × 1 × 1 = 1
0
0
0
0
0
0
0
= (1 + 1) × 1 (iv) (8 ÷ 6 ) – (4 ÷ 3 )
0
0
0
0
= 2 × 1 = 2 = (1 ÷ 1) – (1 ÷ 1)
(iii) (1 + 2 + 3 ) × 7 0 = 1 – 1 = 0
0
0
0
= (1 + 1 + 1) × 1 = 3 × 1 = 3
4 × 4 6 ()5 520
5
Example 4: Simplify: (i) (ii) (iii) (3 ) × 3 × 3 7
– 2 7
3
40 55
4 7 55
5
4 × 4 6 ()5 520 5 20 5× 5 100
Solution: (i) = 4 5 + 6 – 7 = 4 11 – 7 = 4 = 256 (ii) = = = 5 100 – 95 = 5 = 3125
5
4
40 55
4 7 55 5 40 55+ 5 95
1 1
(iii) (3 ) × 3 × 3 = 3 – 14 + 3 + 7 = 3 – 14 + 10 = 3 = =
7
3
– 4
– 2 7
3 4 81
p   3 2   7 0  q  2
Example 5: If =   ÷   , find the value of .
q   2   9  
p

p   3 2   7 0 3 2 9 9
Solution: =   ÷   = ÷1 = ÷ =1 [a = 1]
0
q   2   9 2 2 4 4
q 4
⇒ =
p 9
 q  2   4 2 16
⇒   =   = 81
  9

p
Exercise 6.2
1. Find the value of:
 −  1 7  −  1 4
(i) (–3) ÷ (–3) 2 (ii)   ÷   (iii) x ÷ x (iv) (4) ÷ (4) 7
5
9
4
5
 2   2 
7 4
(v) a ÷ a (vi) (–12) ÷ (–12) 4 (vii) (viii) (–b) ÷ (–b) q
11
p
11
6
7 4
2. Simplify the following.
 7  3  7  4
(i) 2 × 2 (ii) 8 × 8 3 (iii) a × a 7 (iv)   ×  
2
4
3
5
 5   5 
 −  1 2  −  1 3
(v) (–9) × (–9) (vi) x × x q (vii)   ×   (viii) a × a 3
p
3
m
 5   5 
3. Express as a single power.
(i) p × q (ii) 3 × 2 8 (iii) a × b (iv) 7 × 2 9
9
x
x
m
8
m
(v) 4 · 2 (vi) (–5) · (–3) a (vii) a × a (viii) 5 · a 3
a
x
x
m
m
3