7.3 Multiplication Properties of Exponents

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7.3 Multiplication Properties of Exponents

• Algebra 2.0

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Main Idea

• This lesson is the beginning of simplifying
  exponential expressions without doing any kind of
  solving.
• For these kinds of problems we simplify.
• We may evaluate if we are given values to
  substitute in OR our numbers are constants and
  not variables.

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Simplifying Exponential Expressions

• An exponential expression is completely
  simplified if
• No negative exponents
• The base does not repeat
• No powers to powers
• No parentheses raised to a power
• All numbers are reduced

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Product of Powers Property

• Product of Powers Property if the base are the
  same, add the exponents.

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Ex 1 Products of Powers
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Practice 1
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Power of Power Property

• Power of Power Property if a power is raised to
  another power, multiply the exponents.

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Ex 3 Finding Powers of Powers
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Practice 3
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Power of Product Property

• Power of Product Property if there are
  parentheses, distribute the power.

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Ex 4 Finding Powers of Products
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Practice 4
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Review

• If you are multiplying two bases that are the
  same, what operation do you do to their
  respective exponents?
• If you are raising a power to another power, what
  operation do you do to the respective exponents?
• If you are raising a product to a power, then
  what do you do with the exponent?