Page 117 - Maths Skills - 7

Exponents and Powers 115

MIND MAP

Exponents and Powers

7 exponent

10 →
Base
Power
Power of Integers 10 Base
7 Exponent
10 Power
7
i.e. Power Base + Exponent

Laws of Exponents
1. a × a = a m + n
m
n
i.e. 2 × 2 = 2 5 + 3 = 2
8
5
3
3 × 3 = 3 5 + (–3) = 3 = 3 2
–3
5–3
5
2. a ÷ a = a m – n
n
m
Positive Integer Negative Integer i.e. 5 ÷ 5 = 5 (3 – 2) = 5
2
3
1
2
4
a +ve (a) even number +ve 3 ÷ 3 = 3 (4 – 2) = 3 2
b
Here, a +ve integer (a) odd number –ve 3. (a ) = a mn
m n
5 2
b any number Here, a –ve integer i.e. (5 ) = 5 5 × 2 = 5 10
4. a × b = (ab) m
m
m
i.e. 2 × 3 = (2 ×3) = 6 3
3

3
3
m
m m  a 
5. a ÷ b =  
 b  3
i.e. 5 ÷ 3 =   5  
3
3
Reciprocal of Rational Number  3 
6. a = 1
0
p i.e. 7 = 1, (–8) = 1
0
0
q is a non-zero rational number 1
p  p  −1 7. a =
–n
then, reciprocal of =   q   a n
q
  1 1
–2
q i.e. 6 = 2 =
= p 6 36