Laws of Exponents
Laws of Exponents includes laws of multiplication, division, double exponents,zero exponent etc.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.
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.
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
