Page 109 - Maths Skills - 7

Exponents and Powers 107

Exercise 6.1

1. Write the following in the exponential form.

(i) (–7) × (–7) × (–7) × (–7) × (–7) × (–7) (ii) 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5
(iii) (–104) × (–104) × (–104) (iv) (–7)
2. Write the base and exponent for each of the following.

(i) 8 14 (ii)  9  2 (iii) (8.25) (iv) (–7) (v) (0.01) (vi) (–1) 16
5
7
1
 
3. Find the value of.  3 
(i) 5 × 2 (ii) 19 (iii) (–3) (iv) 1 63
2
5
5
3
(v) (–7) × (3) (vi) (–12) (vii) 8 × (–8) (viii) (–1) × (–1) 65
4
111
3
2
1
3
4. Express in exponential form.
(i) 81 (ii) –1331 (iii) 1024
256
5. Fill in the blanks.
 1  4
2
3
7
2
(i)  −  = ___ (ii) (–9) = ___ (iii) 0 = ___ (iv) (–5) × (–5) = ___
 4 
6. Find the value of x, when:
(i) 3 = 729 (ii) –5 = –78125 (iii) 6 = 1296
x
x
x
LAWS OF EXPONENTS
The laws related to exponents and powers are as follows:
1. If a is any non-zero integer and m and n are whole numbers then a × a = a m + n
n
m
For example, 3 × 3 = (3 × 3) × (3 × 3 × 3 × 3) = 3 × 3 × 3 × 3 × 3 × 3 = 3 = 3 2 + 4
2
4
6
2. If ‘a’ is any non-zero integer and m and n are whole numbers then a ÷ a = a m – n (Here m > n)
m
n
2222×××
For example, 2 ÷ 2 = = 2 × 2 = 2 = 2 4 – 2
2
2
4
22×
3. If ‘a’ is any non-zero integer and m and n are whole numbers then (a ) = a mn
m n
For example, (3 ) = 3 × 3 × 3 = (3 × 3) × (3 × 3) × (3 × 3) = 3 = 3 2 × 3
2
6
2
2
2 3
4. If ‘a’ and ‘b’ are two non-zero integers and is a whole number then a × b = (ab) m
m
m
For example, 3 × 4 = (3 × 3) × (4 × 4)= (3 × 4) × (3 × 4) = (3 × 4) = 12 2
2
2
2

5. If ‘a’ and ‘b’ are two non-zero integers and is a whole number then Fact-o-meter
a ÷ b = (a ÷ b) m � a × a = a m + n
m
m
n
m
22222×××× m n m – n
For example, 2 ÷ 3 = � a ÷ a = a
5
5
33333×××× � (a ) × a mn
m n
m
m
2 2 2 2 2  2 5 � a . b = (a . b) m
= ×××× =   = (2 ÷ 3) 5 m m () m
a
3 3 3 3 3  3 � a ÷ b = b
� a = 1
0