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# Laws of exponents

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Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations are called the “Laws of Exponents”

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### Laws of exponents

1. 1. Laws of ExponentsWhenever we have variables whichcontain exponents and have equal bases,we can do certain mathematicaloperations to them. Those operationsare called the “Laws of Exponents”bxb = base x = exponent
2. 2. Laws of Exponents( )( )mnnmnmnmmmmmnnmmmmnmnmxxxthenmnifbxxxthennmifayxyxxxyxxyxxx−−+=>=>====⋅1,.5,.5.4.3.2.1
3. 3. Other Properties of Exponents10=xAny single number or variable is always tothe first power( )1111122233 xxxaa ====xx11=−
4. 4. Basic Examples=⋅ 32xx =+32x 5x( ) =34x =⋅34x 12x( ) =3xy33yx
5. 5. =3yx33yx=47xx=−147x 3x=75xx=−571x 21xBasic Examples
6. 6. More Examples=⋅ 4372 aa ( ) =⋅ +4372 a 714a=⋅⋅− 232285 rrr ( ) =⋅⋅− ++ 232285 r 780r−( ) =33xy =3333 yx 3327 yx=232ba=222232ba2294ba( ) =3522 nm =⋅⋅⋅ 3532312 nm =15632 nm 1568 nm=xx28 4=−128 14x 34x=5339zz=−35139z=213x 23x
7. 7. More Examples=⋅ 22373 xyzzyx ( ) =⋅ +++ 21121373 zyx 33421 zyx( ) =−⋅⋅− 32238 xyxyxy ( ) =−⋅⋅− ++++ 312111238 yx 6348 yx( ) ( ) =2223223 xyyx ( )( ) =⋅⋅⋅⋅⋅⋅ 22212123222123 yxyx=⋅ 426449 yxyx ( ) =⋅ ++ 462449 yx 10636 yx=32335abba=⋅⋅⋅⋅⋅⋅32313131333135baba=63339335baba=633927125baba=−−363927125ba3627125ba
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