EXPONENTS AND MULTIPLICATION 4-7

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EXPONENTS ANDMULTIPLICATION4-7
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Review

• What are exponents?
• Exponents are numbers that show how many times a
  base is used as a factor.
• How do we use exponents?
• Exponents will tell us how many times to multiply
  the base number.
• 43 ? exponent
• base

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Examples

• 24
• 2 x 2 x 2 x 2
• 4 x 2 x 2
• 8 x 2
• 16

• 63
• 6 x 6 x 6
• 36 x 6
• 216

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PART IMultiplying Powers with the Same Base

• Youve already learned how to use exponents to
  indicate repeated multiplication.
• What happens when you multiply two powers with
  the same base?
• Ex. 72 73

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Multiplying Powerswith the Same Base contd

• Ex. 72 73
• (7 7) (7 7 7)
• 75
• Notice that 72 73 75,
• So, when you multiply powers
• with the same base, you can add
• the exponents.
• 72 73 72 3 75

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Rule for Multiplying Powers with the Same Base

• To multiply numbers or variables with the same
  base, add the exponents.
• Arithmetic Algebra
• 23 24 am an
• 23 4 am n
• 27

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ExamplesNote If there is no exponent, it is
automatically a one.

• 3 33

• a5 a b2

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PART IIFinding a Power of a Power

• You can find the power of a power by using the
  rule for Multiplying Powers with the Same Base
  like in Part I.
• (72)3
• (72)(72)(72) Notice that you can raise
• 72 2 2 a
  power to a power by
• 76 multiplying the
  exponents
• 
  (72)3 72 3 76

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Finding a Power of a PowerTo find a power of a
power, multiply the exponents.

• Arithmetic
• (23)4
• 23 4
• 212

• Algebra
• (am)n
• am n

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Examples

• (32)3

• (a6)2