Download 3.1 Solving Equations Using Addition and Subtraction

7-1 Multiplying Monomials
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
A monomial is a number, a variable, or a product of a
number and one or more variables in which there are
no variables in a denominator,
4
x
X
no variables under a radical sign (√),
4x
X
and any exponents on the variables are positive
integers. x 3
X
Monomials that are real numbers are called constants.
Determine whether each expression is a monomial. Explain.
4
5
Yes, it is a real number.
xy
No, it involves addition.
x 5 y2
No, it is has a negative power.
x3 y 4
Yes, the variables are a product.
x
y
No, it is has a variable in the denominator.
a b
No, it involves subtraction.
Today’s lesson involves simplifying monomials involving
powers. To simplify these expressions you will need to
memorize the multiplication properties of exponents.
Recall an expression like 43 is called a power.
base 
43  exponent
word form: four to the third power
four cubed
factor form: 4 • 4 • 4
simplified form: 64
Simplify.
x3  x2  x  x  xx  x
 xxxxx
How can you
get this
answer without
 x5
writing the
To multiply powers that have the factored
same base, add the exponents.
Onform?
tonight’s
x3  x2  x32
 x5
homework, you
must show
this support
work!
PRODUCT OF POWERS PROPERTY
Simplify.
Example 1
Example 2
y 5  y3
 a  a 3
Example 3
Example 4
3
4
y y y
5
Example 5
4ab6  7 a2b3 
x 5  y2  x 7  y
Example 6
 4ab2c3  6a5b4c2 
Simplify.
Example 2
Example 1
y 5  y3  y 5  3
 a  a 3    a  13
  a a a a
 y8
 a4
Example 4
Example 3
3
4
5
y y y  y
3 4  5
 y12
x5  y2  x7  y  x57 y21
 x12 y3
Simplify.
Example 5
4ab6  7 a2b3 
4 7 a1  a2 b6  b3 
 28a12 b63 
Example 6
 4ab2c3  6a5b4c2 
 4  6a1  a5 b2  b4 c3  c2 
24a15 b2 4 c32 
3 9
 28a b
No
multiplication
dots in answer!
24a6b6c5
Simplify.
y   y2  y2  y2
2 3
How can you
get this
 yyyyyy
answer
6
y
without
writing the
To find a power of a power,
factored
multiply the exponents.
On form?
tonight’s
homework, you
3


2
3
must show
y2  y
this support
 y6
work!
 
POWER OF A POWER PROPERTY
Simplify.
Example 8
Example 7
 2 
2 3
23
  2 
   26
 64
m 
5 4
m54 
 m20
Example 9
x 
4 3
 x2  x 43  x2
 x12  x2
 x122
 x14
POWER OF A PRODUCT PROPERTY
To find the power of a product, find
the power of each factor and multiply.
Simplify.
 3xy2   32  x2  y2
 9x2 y2
The power is
given to each
factor inside
the
parentheses!
Simplify.
Example 11
Example 10
2w 6  26 w 6
3xy4 34 x4 y 4
 81x 4 y 4
6
 64w
Example 12 Express
the area as a monomial.
4ab
Example 13 Express the
volume as a monomial.
5xyz
4ab
Area  s2
 4 ab 2
 42 a2b2
 16a2b2
5xyz
5xyz
Volume  s3
 5xyz 3
 53 x3y3z3
 125x3 y3z3
Using More Than One Property to Simplify.
Example 15
Example 14
3x 
4 2
3
2 42
3




6 3
3
x  3 x
x
 3c  c5   3 c63  c5
 9x8  x3
 27c18  c5
 9x83
 27c185
 9x11
 27c23
Example 16
2
4 2 53
7  x23y53 2x7 y 7
x y
2xy 
3
6
2 6 15 7 7
 x y 2x y
3
2
 2x67 y157
3
4 13 22
 x y
3





Memorize the Properties of Exponents
PRODUCT OF POWERS PROPERTY
To multiply powers that have the same base, add the
exponents.
POWER OF A POWER PROPERTY
To find a power of a power, multiply the exponents.
POWER OF A PRODUCT PROPERTY
To find the power of a product, find the power of each
factor and multiply.
7-A2 Pages 361-362 # 16–24,29,39–45,48.
Algebra
rocks!