Math 10

4.2 Notes

Exponent Laws

Exponent Laws tells us what to do with the exponents (if we are asked

to multiply or divide powers). L U\wS ose. j us+ -h ('(1< S o..V-<!.{S )

There are 6 Exponent Laws that you must know.... S\)we ~ ov\ ..t- net ve.+0 \JJ (l t- ~ OLA t- \ ()~

. CotlculOl-h'O(1\S .#1 - Multiplying powers with the same base

. \ \0.6

~if +2- ~Ex: [(2x)4(2x)2]= ( ~:L ~(~~)

LJ L-J

ba~~

(95)(9-2) =5 + l-2.) q3Ex: 9 -~.

#2 - Dividing powers with the same base

a=l=-O·Ex: 75 =

72

Same as:

1!:)-2.. - 13

G-~~-~---:3)~If ~ ;f:¥~/t-(o-3

)L

I\... o. ~.o..~V'I()+ eq..uu \2<.,,0 .

Ex: (2X)3 =(2xr2

t bo.>.t \ ~ ·a){

* *Another way to solve this question, is to write (2xr2 as apositive exponent:

~( c?- ~ )

Exponent Law Worksheet: Do Part 1

,- .

#3 - A Power Raised to a Power

Ex: (23)3 = :1303"" ;) q

Same as: (~'f-?- ~ ?- ) ( ~ 'f- ?- " ~ ') ( ~ 'f.. ;l'f- ~) .~

Ex: (52)3 = (:) ) -a"'3, ~ 5 (0

( L\-)(3) (- ~) _ IJ - l,Ex: [(4X)2]3 = ~1

( Lt 1-- /' 3 '" (+)(.) 10

The last two laws deal with situations where you do NOT have theo.

same bases, But we have already seen these rules before l~-. - -e.'i. ::

IL\0Ex: r 21\0=

l31

Ex: [~ r =

#4 - Power of a Quotient

[~~" = :nn .L-_---b~~~D -----'U if __.: ~. 4..

~ ~ _ Y- Ex: rv:14 = ,~ ~;)?-- -9 L 2xJ ~ ~ >( '\ \ (0 ')( 4

~~->, \)04G'· -tv ev\-K( an

e.x txJ'f\..tn+ Of\ "I tJvt ('Cct \ (ct \ ut-\1) (' ~

J.4: :l [b] ~ ~ lb

~(£1q~\6

I

\R5

#5 - Power of a Product

(ab)-DJ= an'bn

{\J{~-thi~ .' (\$\ de \?rttc\.u-\ s i-S (~~~G~ to expo()R()t

mU. \t~P~ ¥nVD~h2 f}a~,.., i\ 2-

Ex: (2x) = (j.. "or.. _ \" ~

( ~X)( ~'X) ~3 '3> ~J j = ~1-j~3 lq)(-3) _-3 -\ ~X~~t =-'1~

m'-' \-hp'j

(pow -ov vll:~d ~ OtpouJ-t()

Ex: (3y)3 =

10'1 _

::i....."3(j 12-

Summary: EXPONENT LAWS

Multiplying powers with the same base (am )(an) rn+n= aDividing powers with the same base am m-n= a

an

A Power Raised to a Power (am t = am-n

Power of a Quotient n n~ = ~b bn

Power of a Product (ab)" = an·bn

Zero Exponent aD -1

f\Nt) •. 'O--n \'" ---'0.-("\1l:Jo.-r;\le.., \ 0.-(\-e.XpOV\ t f\-\- S : (),-n

Applying More than 1 Law:

Exf~:l3= (J ~-~)-3 _

t c\.ea\ w-\+\\~P(){\-e(\t-S \0S\cU bitt lkits '

EX:~~3 =

[ -l-l\-+,,]-3

[-c-J-3(-3; -3

~ ['(\1\ \hpl:)IL J- 2.. 1--1--1")-1,----, L\

L-.-~-\2.. . \0 cJ..!

::Lj = L~

Exponent law Worksheet: Do Part 2

Text Book: p. 169 #4 and 5