Laws of Exponents
Laws of Exponents includes laws of multiplication, division, double exponents,zero exponent etc.
VIDEO
There are 8 Laws of Exponents.
Multiplying powers with same base
1) If the bases are same and there is a multiplication between them then, add the exponents keeping the base common.
Examples :
i) 3
3 x 3
2
= 3
(3 + 2) = 3
5 [exponents are added]
ii) b
5 x b
-2
= b
5 +(-2) [exponents are added]
= b
5-2
= b
3
(iii) (-6)
3 x (-6)
2
= (-6)
3+2
= (-6)
5
(iv) 8
10 x 8
12
= 8
10+12
= 8
22
Dividing powers with the same base
If the bases are same and there is a division between them then, subtract the 2nd exponent from the 1st keeping the base common.
Examples :
(i) 4
5 / 4
3
= (4 x 4 x 4 x 4 x 4)/(4 x 4 x 4)
= 4
( 5 – 3)
= 4
2
(ii) p
6 ÷p
2
= p
6 - 2
= p
4
(iii) 8
15 /8
12
= 8
15-12
= 8
3
(iv) 15
6 /15
8
= 15
6-8
= 15
-2
(v)(5/2)
9 ÷ (5/2)
4
= (5/2)
9-4
= (5/2)
5
Power of a power
3) If there are double exponents then, multiply the exponents and keep the base same.
( am ) n = a(m x n ) = amn
Examples :
(i) (2
3 )
2
= 2
( 3 x 2 ) [ multiply the two powers]
= 2
6
(ii)(-8
4 )
2
= (-8)
(4 x 2) [multiply the two powers]
= (-8)
8
(iii) (y
-2 )
-3
= y
(-2 x -3)
= y
6 [ negative times negative --->positive]
Zero Exponent
4) Any number with exponent zero ,the answer is 1.
Example :
(i) (1000)
0
= 1
(ii) a
0
= 1
(iii) (-25)
0
= 1
Exponent 1
5) If the exponent is 1 then the number itself is the answer.
Example :
(i) 20
1
= 20
(ii) b
1
= b
(iii) (2000)
1
= 2000
Negative Exponent
6) If the exponent is negative so to make it positive write the reciprocal of it.
Example :
i) 4
-2
= 1 / 4
2
= 1 / 16
2) 1 / 3
-2
= 3
2
7) Two different bases have same exponents then bring the two bases under common parenthesis and keep the same exponent.
am x bm = (ab)m
am ÷ bm = (a/ b)m
Example 1 :
(i) 2
2 x 3
2
= ( 2 x 3 )
2
= 6
2
= 6 x 6 = 36
(ii) 6
2 ÷ 3
2
= ( 6/3)
2
= 2
2
= 2 x 2 = 4
(iii) 3
4 x 3
-3
= 3
4 ÷ 3
3
= 3
4 / 3
3
= 81 / 27
= 3
Exponents
• Laws of Exponents
• Rational Exponents
• Integral Exponents
• Scientific notation
• Solved examples on Scientific Notation
• Solved Examples on Exponents
Exponents to Home Page