Algebra 1
Week 3.3
Page 335
Multiplication Properties of Exponents, Category 5 (A.11A), PH 8.3
In this lesson you will learn how to multiply exponential terms which have the same base. The base of an
exponential term could be a number or variable, the power is the exponent.
34
𝑥6
Example:
base
exponent (power)
base
exponent (power)
When you have exponents, there is an easy way to understand what they represent by writing them in
expanded form.
Example 1
92 ∙ 95
(9 ∙ 9)(9 ∙ 9 ∙ 9 ∙ 9 ∙ 9)
Expand each exponential expression
9∙9∙9∙9∙9∙9∙9
How many times is 9 being multiplied?
97
Try It
Simplify using expanded form
a) 45 ∙ 43
b) 𝑡 4 ∙ 𝑡 6
Notice the above problems can also be simplified by adding the exponents. This is the rules:

When you multiply exponential terms which have the same base, you add the exponents.

𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛

𝑝5 ∙ 𝑝2 = 𝑝 5+2 = 𝑝7
Multiplication property with bases which are variables

33 ∙ 32 = 3
Multiplication property with bases which are numbers
3+2
The powers being multiply have the same base, 𝑎, so you add the exponents
= 35 = 243
Both methods yield the same solution:
32 ∙
33
=
32+3
= 35 = 243
(3 ∙ 3)(3 ∙ 3 ∙ 3) = 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 = 35 = 243
Solved using multiplication property of exponents
Solved using Expanded Form
Algebra 1
Week 3.3
Page 336
Try It
Simplify using Multiplication Property
a) 𝑑14 ∙ 𝑑−6
b) 𝑑 −5 ∙ 𝑑12
Multiplying exponentially terms which have coefficients
(2𝑥 3 𝑦 2 ) (5𝑥𝑦 4 )
10 (𝑥 3 𝑦 2 ) (𝑥𝑦 4 )
Multiply the coefficients
10 (𝑥 3 ∙ 𝑥) (𝑦 2 ∙ 𝑦 4 )
Multiply the terms that have the same base
10 (𝑥
3+1
) (𝑦
2+4
)
Add the exponents when multiplying terms with the same base
10 𝑥 4 𝑦 6
Try it
a)
(6𝑥2𝑦 3 ) (– 8𝑥 4 𝑦 5 )
Example 2
( 5𝑎3 𝑏 −2 ) (– 4𝑎−2 𝑏 5 )
−20 ( 𝑎3 𝑏 −2 ) ( 𝑎−2 𝑏 5 )
Multiply the coefficients
−20 ( 𝑎3 𝑎−2 ) ( 𝑏 −2 𝑏 5 )
Multiply terms which have the same base
−20 ( 𝑎3−2 ) ( 𝑏 −2+5 )
Add the exponents when multiplying terms with the same base
−20 ( 𝑎1 ) ( 𝑏
−20 𝑎 𝑏 3
3
)
Algebra 1
Week 3.3
Try it
b) (– 7𝑚5 𝑚−6 ) (9𝑚 − 2𝑚8 )
Example 2
a) Simplify the expressions 3𝑦 5 ∙ −2𝑦 −3
3𝑦 5 ∙ −2𝑦 −3
−6 𝑦 5 ∙ 𝑦 −3
Multiply the coefficients
−6 ( 𝑦 5+(−3) )
Add the exponents
−6𝑦 2
b) Simplify the expressions 5𝑦 −5 ∙ 2𝑥 2 ∙ 3𝑦18
5𝑦 −5 ∙ 2𝑥 2 ∙ 3𝑦 18
30 𝑦 −5 ∙ 𝑥 2 ∙ 𝑦 18
Multiply the coefficients
30 (𝑦 −5+18 )(𝑥 2 )
Add the exponents
30 𝑦 13 𝑥 2
Try It
c) Simplify the expressions 4𝑣 −5 ∙ 2𝑧 2 ∙ 3𝑣 8
d) Simplify the expressions 5𝑎3 ∙ 2𝑎−2 ∙ 3𝑎12
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Algebra 1
Week 3.3
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Algebra 1
Week 3.3
Page 339
Practice: Multiplication Properties of Exponents, Category 5 (A.11A), PH 8.3
Name: __________________________________
Period: _______
Simplify using Multiplication Property of Exponents and prove with Expanded Form
1. 53 ∙ 54
2. 𝑏 4 ∙ 𝑏 8
Simplify using Multiplication Property
3. 𝑦 8 ∙ 𝑦 −5 ∙ 𝑥 3
4. 𝑣 −3 ∙ 𝑣 5 ∙ 𝑣 11
Simplify the expression
5. (4𝑔4 )(−2𝑔−2 )
6. (8𝑛7 )(3𝑛−2 𝑚4 )
7.
(0.5𝑥 9 )(2.5𝑥 −1 )(4𝑥 −4 𝑦 4 )
Algebra 1
Week 3.3
Page 340
Express your understanding in words.
8. Given an algebraic expression, how do you determine the coefficient, the base and the exponent?
EOC Connection, Category 5 (A.11A)
9. Which expression represents the area of a rectangle with sides measuring 2x2y4z units and 5xy4z3
units?
F 7x2y8z3 units2
G 7x3y8z4 units2
H 10x3y8z4 units2
J 10x2y8z3 units2
10. Which expression represents the area of a rectangle with sides measuring x2y and 2xy2?
A 2x3y3
B 2x2y2
C 4x4y3
D 4x3y4