9-2: Dividing Monomials

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9-2 Dividing Monomials
OBJECTIVES You will simplify expressions
involving quotients of monomials and those
containing negative exponents.
Three new rules about exponents in this section.
When same bases are divided, the result is that
base to the difference of the powers. The
numerators power minus the denominators power
goes on the answer. So, x(8 - 5) x3.
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9-2 Dividing Monomials
EXAMPLE 1 Simplify
METHOD LONG
METHOD SHORT
Write it all out the long way.
Remember, this can be written like this
Now use the Quotient of Powers rule.
y(4 - 2)z(3 - 2) y2z
Rewrite without all the ones.
(y)(y)(z)
Simplify.
y2z
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9-2 Dividing Monomials
Now look at this.
We can look at it in two different ways
ONE Long Way
TWO Quotients of Powers
b(5 - 5)
1
b0
This just goes to show us what anything to a zero
power yields 1. Guess what the next rule is.
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9-2 Dividing Monomials
Just remember, anything to the zero power yields
1, except zero itself. Zero itself to the zero
power is undefined. Also, anything over itself
yields 1. So, 1 and q0 1.
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9-2 Dividing Monomials
Here is a walk-through for the next rule.
We can look at it in two different ways
ONE Long Way
TWO Quotients of Powers
r(3 - 7)
r - 4
When asked to simplify expressions, you must get
rid of all negative exponents. From the
information above, you can determine what is
needed to get rid of the negative exponents. The
next rule defines this.
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9-2 Dividing Monomials
The way I think about this rule is this If a
power is negative, it is unhappy where the base
is. The negative power want the base to move. In
math, the only place the base can move to is
either to the numerator or the denominator. Once
the base has moved, the exponent becomes
happy. This only works with negative
EXPONENTS! So, and
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9-2 Dividing Monomials
EXAMPLE 2 Simplify
Get like numbers and variables grouped together
to make it easier. You should do this when you
copy the problem down from the book to save time.

Simplify each part and multiply them back
together.



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9-2 Dividing Monomials
EXAMPLE 3 Simplify
Use Powers of Powers and Powers of Products rules
first.
Simplify the powers and make the exponent on the
5 happy.
Get like numbers and variables grouped together
to make it easier. Rewrite the numbers to powers
with calculator.
Four ps in the top cancel four ps in the
bottom, leaving a one in the top and two ps in
the bottom.
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9-2 Dividing Monomials
HOMEWORK
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