1-3
A. Vocabulary:
◦ Power – product in which the factors are the same
◦ Exponent – tells how many times the base is
multiplied
◦ Base – the number that is multiplied
◦ Exponential notation – an expression that is written
with exponents
B. Writing out an expression with exponential
notation:
22 = 2 x 2
35 = 3 x 3 x 3 x 3 x 3
n4 = n x n x n x n
y3 = y x y x y
2y3 = 2 x y x y x y
(the exponent is only connected to the y,
so that is the only thing that is expanded)




1.
2.
3.
4.
54
b3
2x3
12y4
C. Writing in exponential notation:
7 x 7 x 7 x 7 = 74
n x n x n x n x n x n = n6
3 x m x m = 3m2
2 x y x y x y x y = 2y4





1.
2.
3.
4.
5.
9x9x9
y·y·y·y·y
4xnxnxnxnxn
15 · x · x · x · x
10 x b x b x b
Note:
You can also “evaluate” problems that
include exponents

ex. y4 + 3 for y = 2
24 + 3
2·2·2·2+3
16 + 3
=
19
End of Part 1

Up until now, all exponents were connected
to only one number/variable, known as the
base
2y5

When an expression inside parentheses is
raised to a power, everything inside the
parentheses becomes the base
(2y)5

A. To solve problems with exponents on the
outside of the parentheses, you must
connect/distribute the exponent to
everything on the inside
1. (3a)4
2. (5y)3
34 · a4
53 · y3
81 · a4
125 · y3
81a4
125y3


B. You can also do this same thing with
evaluating:
Example:
(4m)3 for m = 2
43 · m3
43 · 2 3
64 · 8
512
1. (10y)2
2. (6m)3
3. (8n)5 for n=2
End of Part 2

C. When you have exponents both inside and
outside of the parentheses:
◦ You must multiply the exponents
(52)3
Multiply your exponents
56 = 15,625
1. (84)3
2. (k7)5
3. (3a2)5
A. If you have the same base in the top and
bottom of the fraction, and they have
exponents, you can simplify
B. As long as they are the same base, you will
take the top exponent and subtract the bottom
exponent
35
Take the exponents and
subtract…5 – 3 = 2
33
32

1. 78
75
2. b12
b4
3. x
x3

C. If you do not have the same base, you
cannot subtract the exponents
m3
t5

D. If there are multiple bases, combine your
like bases and leave the rest where they were
Here are
your like
bases…
subtract the
exponents
x6 y 2 =
x3z4
x3 y 2
z4

1. 126145
124
2. a3b8
b2c9
3. 3xy
12y