Transcript Section 5.4
5.4
Exponent Rules and Multiplying
Monomials
1. Multiply monomials.
2. Multiply numbers in scientific notation.
3. Simplify a monomial raised to a power.
Objective 1
Multiply monomials.
23 • 2 4
23 means
three 2s.
23
222
27
24
2222
24 means
four 2s.
Since there are a total of seven 2s multiplied,
we can express the product as 27.
Keep the base and add the exponents
Product Rule for Exponents
If a is a real number and m and n are integers,
then am • an = am+n.
Multiply:
2
9 9
5
4
6
3 3
97
310
When an equation in one variable is solved the answer is a point on a line.
4 2 4 6
4 8
3 3
4
48
5
39 39
3
5
2a 7a 14a
8
Multiplying Monomials
1. Multiply coefficients.
2. Add the exponents of the like bases.
3. Write any unlike variable bases unchanged in
the product.
Simplify:
3
5x 7 x
2
2
4
5 3
35x
25 81 2025
5
2x3 5x3
3a line.
When an equation in one variable is solved the answer3is a point on
2 x 5x
10x
6
1 2 5
3 2 5
k m km n k
4
6
3
7x 3
5 8 4
k m n
36
Objective 2
Multiply numbers in scientific
notation.
Monomials:
Scientific notation:
4a3 2a6 4 2a36
3
6
3 6
4
10
2
10
4
2
10
8a9
8 109
Multiply and write result in scientific notation:
3
4
4.5
10
5.7
10
25.65 107
2.565 108
When an equation in one variable is solved the answer is a point on a line.
3
6
6.2
10
3.1
10
19.22 10 3
1.922 10 2
Objective 3
Simplify a monomial raised to a
power.
x
2 5
2
2
2
2
x x x x x
2
x
10
A Power Raised to a Power
If a is a real number and m and n are integers,
then (am)n = amn.
4a
3
4a 4a 4a 4 3 a 3 64a3
Raising a Product to a Power
If a and b are real numbers and n is an integer,
then (ab)n = anbn.
2x y
3 2 4
4 12 8
12 8
2 x y 16 x y
Simplifying a Monomial Raised to a Power
1. Evaluate the coefficient raised to that power.
2. Multiply each variable’s exponent by the power.
Simplify:
3x y
2 32
2 3 5
2x y
2 x 10 y 15
9x 4 y 6
When an equation in one variable is solved the answer is a point on a line.
x y
2
x y
2
3 2 5
x4y2
x 15 y 10
Simplify:
2x y 2xy
2
4
23
3x4 y2z yz4
24 x 8 y 4 23 x 3 y 6
2 7 x 11 y 10 128 x 11 y 10
When an equation
point6on3a line
5 . 20
3 in one 5variable is solved the answer 3is a 12
3 x y z y z
33 x 12 y 11 z 23 27 x 12 y 11 z 23
x y x y
5 23
2 32
x 15 y 6 x 4 y 6
x 19 y 12
7
3
6
b
3
b
Simplify.
a) 18b 21
b) 18b10
c) 9b 21
d) 9b10
5.4
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Slide 5- 17
7
3
6
b
3
b
Simplify.
a) 18b 21
b) 18b10
c) 9b 21
d) 9b10
5.4
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Slide 5- 18
Simplify. 4 y
2
5 y
3 4
a) 20 y 9
b) 20 y 20
c) 2500y 9
d) 2500y14
5.4
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Slide 5- 19
Simplify. 4 y
2
5 y
3 4
a) 20 y 9
b) 20 y 20
c) 2500y 9
d) 2500y14
5.4
Copyright © 2011 Pearson Education, Inc.
Slide 5- 20