Math, asked by Shevor, 1 year ago

all laws of exponents with 2 examples each

Answers

Answered by Himanshunavik
10
The laws of exponents are explained here along with their examples.

Multiplying powers with same base. For example: x² × x³, 2³ × 2⁵, (-3)² × (-3)⁴ ...Dividing powers with the same base. For example: ...Power of a power. ...Multiplying powers with the same exponents. ...Negative Exponents. ...Power with exponent zero. ...Fractional Exponent.

Answered by Taanvi
17
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.
a m x a n = a ( m + n )
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.
a m ÷ a n = a ( m - n )
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
= 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.
( a m ) n = a (m x n ) = a mn
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.
a 0 = 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.
a 1 = a
Example :
(i) 201
= 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.
a -m = 1/a m
1/a -m = a m
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.
a m x b m = (ab) m a m ÷ b m = (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
Hope it helps you
please mark as brainliest

Taanvi: if it helped u
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Taanvi: ok no prblm
Taanvi: sorry
Shevor: tq so much
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