Name ______________________
Algebra I
Date __________
Unit 7 Day 1 Exponent Properties involving Products and Quotients
 Today we will learn about properties involved in multiplying and dividing
exponents.
 By the end of class you will be able to multiply and divide expressions with
the same base.
Powers and Exponents
32
4x 3
Example #1 – Fill in the chart below.
Expression
Coefficient
Base
Exponent
x
7a 3
x
 
3
2
 x  3
4
Example #2 – Complete the chart below.
Exponential Form
Expanded Form
84
x3 y 2
(c  14)2
3 x  x  x  x
2 a  a  a bb
  x   x   x   x   x 
 n  3 n  3 n  3
Product of Powers Property – when you multiply powers having the same base,
_______ the exponents.
Examples:
43 45 =
x  x4 x6 =
xy2 × x 2 y × x 3 y 2 =
Power of a Power Property – To find the power of a power, _____________ the
exponents.
Examples:
(-2 5 ) 2 =
x 
4 6
=
x 
2 3
=
Power of a Product Property – To find the power of a product, find the power of
each factor and _____________.
Examples:
(xy) 3 =
(5x) 2 =
(2x 3 ) 2 (2 x 4 ) =
Quotient of Powers Property – To divide powers having the same base,
___________ the exponents.
Examples:
57
54
4
x
x2
10 x 6
2 x2
Power of a Quotient Property – To find the power of a quotient, find the power of
the numerator and the power of the denominator and ______________.
x
 
 y
3
 4 x2 


 5 xy 
7
 x
 
2
3
1
y
5
 y8