Dividing Monomials

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Dividing Monomials
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Objectives

1. Be able to divide polynomials
2. Be able to simplify expressions involving powers
   of monomials by applying the division properties
   of powers.

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Vocabulary
Monomial A number, a variable, or the product of
a number and one or more variables
Constant A monomial that is a real number.
Power An expression in the form xn.
Base In an expression of the form xn, the base
is x.
Exponent In an expression of the form xn, the
exponent is n.
Quotient The number resulting by the division of
one number by another.
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Review Exponents
Repeated multiplication can be represented using
exponents.
To expand a power, use the exponent to determine
the number of times a base is multiplied by
itself.
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Review Multiplying Monomials
Product of Powers When two numbers with the same
base are multiplied together, add the exponents
and leave the base unchanged.
Power of a Product In a product raised to a
power, the exponent applies to each factor of the
product.
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Review Multiplying Monomials
Power of a Power When a power is raised to
another power, multiply the exponents and leave
the base unchanged.
Remember Follow the order of operations when
applying more than one property!
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Quotient of Powers
Simplify
Step 1 Rewrite the expression in expanded form
Step 2 Simplify.
For all real numbers a, and integers m and n
Remember A number divided by itself is 1.
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Power of a Quotient
Simplify
Step 1 Write the exponent in expanded form.
For all real numbers a and b, and integer m
Step 2 Multiply and simplify.
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Example Problems
Apply quotient of powers
Apply power of a quotient
Apply quotient of powers.
Apply power of a quotient.
Apply power of a power
Simplify
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Practice
1. 2.
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Problem 1
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Problem 2
THINK! x2-2 x0 1