LAWS OF
EXPONENTS
Monomial is an expression that is a
number, a variable, or a product of a
number and variables.
Power is the expression of the form xn.
Laws of Exponents
Multiplying Powers:
a a  a
m
n
Power of a Power  a   a
m
n
mn
mn
Laws of Exponents
m
Dividing Powers:
Power of a Product:
a
n
a
a
mn
 ab   a b
m
m m
Laws of Exponents
Power of Zero:
a 
0
1
Examples using the
laws of exponents:
1. x² ·x³= x²+³
2. (x²)³= x²•³
Keep the base
Add the exponents
Keep the base
Multiply the exponents
Examples using the
laws of exponents:
12
Keep the base
x
8 Subtract the exponents
3. 4  x
x
Raise each base to the
4. (xy)³= x³y³ exponent
Then multiply
By definition 25 is the number you would multiply times
itself to get 25 for an answer.
Because we are familiar with multiplication, we know
that 25 = 5
Numbers like 25, which have whole numbers for their
square roots, are called perfect squares
You need to memorize at least the first 15 perfect squares
SQUARE ROOTS
Perfect
square
1
Square
root
Square
root
1 = 1
Perfect
square
81
81 = 9
4
4 = 2
100
100 = 10
9
9 = 3
121
121 = 11
16
16 = 4
144
144 = 12
25
25 = 5
169
169 = 13
36
36 = 6
196
196 = 14
49
49 = 7
225
225 = 15
64
64 = 8