71 Multiplying Monomials

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7-1 Multiplying Monomials
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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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,
no variables under a radical sign (v),

X
X
and any exponents on the variables are
positive integers.
X
Monomials that are real numbers are called
constants.
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Determine whether each expression is a monomial.
Explain.
Yes, it is a real number.
No, it involves addition.
No, it is has a negative power.
Yes, the variables are a product.
No, it is has a variable in the denominator.
No, it involves subtraction.
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Todays 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.
43
base ?
? exponent
word form four to the third power
four cubed
factor form 4 4 4
simplified form 64
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Simplify.
How can you get this answer without writing the
factored form?
To multiply powers that have the same base, add
the exponents.
On tonights homework, you must show this support
work!
PRODUCT OF POWERS PROPERTY
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Simplify.
Example 2
Example 1
Example 4
Example 3
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Simplify.
Example 6
Example 5
No multiplication dots in answer!
No multiplication dots in answer!
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Simplify.
How can you get this answer without writing the
factored form?
To find a power of a power, multiply the
exponents.
On tonights homework, you must show this support
work!
POWER OF A POWER PROPERTY
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Simplify.
Example 8
Example 7
Example 9
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POWER OF A PRODUCT PROPERTY
To find the power of a product, find the power of
each factor and multiply.
Simplify.
The power is given to each factor inside the
parentheses!
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Simplify.
Example 11
Example 10
Example 13 Express the volume as a monomial.
Example 12 Express the area as a monomial.
4ab
5xyz
4ab
5xyz
5xyz
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Using More Than One Property to Simplify.
Example 14
Example 15
Example 16
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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.
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Homework
7-A2 Pages 361-362 1424,29,3948.
Algebra rocks!