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Published byElaine Hall Modified over 7 years ago

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

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To multiply monomials

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Exponent Review Base Exponent

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It means to use 2 as a factor 5 times. What does it mean?

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Exponent Review Base Exponent

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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 What’s 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 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 2 nd 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 What’s 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 3 rd power.

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Example 4 Now, there are no outside exponents. We can multiply the coefficients Then multiply the x’s Then multiply the y’s

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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 6 th power.

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Example 5

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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 What’s the exponent for this b?

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Example 6

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Example 7 Raise everything in the parentheses to the 2 nd 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 3 rd 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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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 MOVE & CHANGE y does not have negative exponent. It stays where it is. Nothing is left on top. We know there is an invisible 1 there.

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Negative Exponents

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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 2 nd 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 11 Move any negative exponents and change to positive.

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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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Move negative exponents and change to positive.

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Example 13

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Example 14

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Move negative exponents and change to positive.

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Example 14

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