Section 6.1 Exponential Expressions

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Section 6.1 Exponential Expressions

• Objective 1 To multiply monomials.
• Objective 2 To divide monomials and
  simplify expressions with
  negative exponents.

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Objective 1

• To multiply monomials

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Exponent Review
Exponent

• Base

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What does it mean?
It means to use 2 as a factor 5 times.
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What does it mean?
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(No Transcript)
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Exponent Review
Exponent

• Base

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What does it mean?
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What does it mean?
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Multiplying with exponents

• When you multiply, add the exponents.

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Example 1
Whats the exponent for this x?
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Example 1
Multiply the coefficients first.
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Example 1
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Example 1
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Example 2
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Example 2
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Raising a power to a power

• When raising a power to another power, multiply
  the exponents.

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Raising a power to a power

• When raising a power to another power, multiply
  the exponents.

Take everything in parentheses and raise it to
the 2nd power.
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Raising a power to a power

• When raising a power to another power, multiply
  the exponents.

Use Distributive Property.
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Example 3
Simplify the coefficient.
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Example 3
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Example 4
Whats the exponent for this x?
Whats the exponent for this x?
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Example 4
Simplify this expression first because it has an
outside exponent.
Take everything in parentheses and raise it to
the 3rd power.
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Example 4
Now, there are no outside exponents. We can
multiply the coefficients Then multiply the
xs Then multiply the ys
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Example 4
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Example 4
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Example 5 (skip)
Start outside the brackets Multiply the two
outside exponents.
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Example 5
Simplify the outside exponent. Raise everything
inside the parentheses to the 6th power.
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Example 5
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Objective 2

• To divide monomials and simplify negative
  exponents.

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Dividing with exponents

• When you divide, subtract the exponents.

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Example 6
Whats the exponent for this b?
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Example 6
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Example 7
Raise everything in the parentheses to the 2nd
power.
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Example 7
Subtract the exponents.
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Example 7
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Example 8
Raise everything in the parentheses to the 3rd
power.
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Example 8
Simplify the denominator.
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Example 8
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Look At This
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Look At This
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Look At This
This is another rule.
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Zero as exponent

• Anything raised to zero power equals 1.

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Review Whole Numbers
Any whole number can be placed on top of 1.
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Review Whole Numbers
Any whole number can be placed on top of 1.
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Review Whole Numbers
Any whole number can be placed on top of 1.
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Review Whole Numbers
Any whole number can be placed on top of 1.
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Review Whole Numbers
Any whole number can be placed on top of 1.
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Review Whole Numbers
Any whole number can be placed on top of 1.
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Fractions
There are 2 parts of a fraction.
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Negative Exponents
When you see negative exponents, think MOVE
CHANGE
Move the base from top to bottom or bottom to top.
Change the exponent to a positive number.
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Negative Exponents
MOVE CHANGE
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Negative Exponents
MOVE CHANGE
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Negative Exponents
y does not have negative exponent. It stays where
it is.
Nothing is left on top. We know there is an
invisible 1 there.
MOVE CHANGE
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Negative Exponents
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Negative Exponents
MOVE CHANGE
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Negative Exponents
MOVE CHANGE
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Negative Exponents
MOVE CHANGE
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Negative Exponents
MOVE CHANGE
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Example 9
Raise everything in the parentheses to the
negative 2nd power.
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Example 9
Move the negative exponents and change to
positive exponents.
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Example 9
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Example 10
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Example 10
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Example 11
Move any negative exponents and change to
positive.
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Example 11
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Example 11
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Example 12 (skip)
Subtract the exponents.
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Example 12
Put under 1 and change exponent to positive.
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Example 12
The variable stays where the bigger exponent was.
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IMPORTANT!

• Your final answer can NOT have any negative
  exponents.
• Remember to move all negative exponents and
  change them to positives.

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All Rules in Symbolic Form
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Example 13
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Example 13
Move negative exponents and change to positive.
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Example 13
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Example 13
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Example 14
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Example 14
Move negative exponents and change to positive.
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Example 14
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Example 14