Notes: Exponential Rules

• Ex]!onent Review- Remember two things:

exponent tells you how many times to multiply
1. You never multiply a base by its exponent. The
4 = 64.
the base by itself. * 4 is NOT 4 x 3. It is 4 x 4 x
3

If a base is negative, it must be in parentheses to use it when you multiply. Otherwise, your
2.
answer will always be negative.
* (-3) 4 means (-1,J (-3J • (-~J ::O t 3) 1
i \
* -3 4 means - ° 0 3 •3 ., '3 :: -
:?s \
n.
YOUR TURN: Evaluate the exponential expressio
3 ~- 8 3. (-6) 3 = - i) l,
s = li 5 2. (~) = 33 -1B
(- to) ~ (- la) -(-La)
3
1. 3
s~o-~
= 7 i C, 5. -2 2 = - '-l 6. 1.13 = I· 33 )
4. 93
~l ~ i ). 1. I~} •I./
9 ·°l ·1
RULES OF EXPONENTS
rn~n
ers am· an= _O= ..i./\----._
• Rul.e I: Product of Pow
Whe n I ti mu
p~ I exponents with ©
the same base, __ _O._ _d= --d~ -- the exponents.

Ex: 4
3
•4
2
=~ Why? ~ • L/ •Lj • Lj • Lj :- ~ 6"
answer.
YOUR TURN: Simplify using exponents in your -11 \'I-
2 5
= {)
7
2) (-4 ) 3
• (-4 )
8 {__
=_,:_. -i~J
1) 3 • 3
_c:- \ 12.
4) (-5 ) 7
X (-5 ) 3
X (-5 )2 =~-.l J~J_
am= °'m-n
Rule 2: Quotient of Powers an
exponents with the same base, sub-tY0crr the exponent
s.
When div1d1rn
36 '2 '2. 3•
Why?• • • • '3\ • 3 - 2v 2-
-~ --- - -
Ex: ii= ~Q-
-~er.
3in•your answ
YOUR TURN: Simplify using exponents

1) ~ = {0 4 2) (-18 ) = ~ IiY) 10
5 (-18 ) 2
~
6 -
(q
•
3)
8
10 + 10 =
4
IO 4) 9 + 9 = 5 9

I
 f'lm,n
Ruic 3: Power ofa Power (am)n =_Y\_____
When finding the power of a powe1·, mI/ Ih Pt/ the exponents.

Ex: = (63)
4
= lo
1
1. Why? ( (o •lo •~) • ( lo · lo • lo) • Clo · l!r Lo) ' ( lo • (o • <e) •
I '1 3 L./

YOUR TURN: Simplify using exponents in your answer.

QI 1.. 15/1.t)
1) (84 ) 3 = __._Q__ 2) (15 2 ) 8 = ___,,_ _

/_11\IL 91b
3) [(-4)6]2 = ~ 4) (93)5 = - ~ -

REVIEW:
,,o
1) (-15) 6
• (-15) 3
• (-15) = (~\ ~ J

3)
C-5)8 = l-s)s 4) (78)2 = l'ID
(-5)3

34. 36 = 3'0
5) (41)5 = w5 6)

7) 65 X 6 2
= lo7 8)
1012
104
,o~ •
9) (-12) 10 + (-12) 2 =
l-12)i 10) 8 5 X 8 = i(o

Chal1enge:

s~ : 5 ~
~
10~ 54. 56
102 X 10 6
11)
10 7
w:10 12) 54

/0
~
75 x 7 3 J..::.._ - 7s 47. 43 Y
-'t.44
13) - 73 - 14) - y(O
7 x7 2 48+ 42

(36)2 _ £ ,2 ~ I 28 - 2 3 x 2 ,.
2-' '2..
2·· :. 2
I

15) 3 16)

•
(33)4 z6.z3.z2