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) 33 x 3 2
= 3(3 + 2) = 35[exponents are added]
ii) b5 x b-2
= b5 +(-2)[exponents are added]
= b5-2
= b3
(iii) (-6)3 x (-6)2
= (-6)3+2
= (-6)5
(iv) 810 x 812
= 810+12
= 822
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) 45/ 43
= (4 x 4 x 4 x 4 x 4)/(4 x 4 x 4)
= 4( 5 – 3)
= 42
(ii) p6÷p2 = p6 - 2
= p4
(iii) 815/812
= 815-12
= 83
(iv) 156/158
= 156-8
= 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) (23)2
= 2( 3 x 2 ) [ multiply the two powers]
= 26
(ii)(-84)2
= (-8)(4 x 2) [multiply the two powers]
= (-8)8
(iii) (y-2)-3
= y(-2 x -3)
= y6 [ negative times negative --->positive]
Zero Exponent
4) Any number with exponent zero ,the answer is 1.
Example :
(i) (1000)0
= 1
(ii) a0
= 1
(iii) (-25)0
= 1
Exponent 1
5) If the exponent is 1 then the number itself is the answer.
Example :
(i) 201
= 20
(ii) b1
= 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) 22 x 32
= ( 2 x 3 )2
= 62
= 6 x 6 = 36
(ii) 62 ÷ 32
= ( 6/3)2
= 22
= 2 x 2 = 4
(iii) 34 x 3-3
= 34 ÷ 33
= 34 / 33
= 81 / 27
= 3
Exponents
• Laws of Exponents
• Rational Exponents
• Integral Exponents
• Scientific notation
• Solved examples on Scientific Notation
• Solved Examples on Exponents
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