Exponents

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Exponents
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As I was going to St. Ives I met a man with seven
wives, Each wife had seven sacks, each sack had
seven cats, Each cat had seven kits kits, cats,
sacks and wives, How many were going to St.
Ives? 
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3
Exponent How many times the base number is
multiplied by itself
2
Base Number The number being
multiplied over and over again
This is read as, 2 to the third power. This
expression is saying 2 times itself 3 times. 2 ?
2 ? 2
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How Do You Read
4 to the second power

• 42
• 83
• 25

8 to the third power
2 to the fifth power
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There are fancy ways to read exponents of two and
three do you know what they are and why we use
these fancy words?

• Any base number to the power of 2 is read as, a
  number squared
• ex 92 is read, nine squared.
• Any base number to the power of 3 is read as, a
  number cubed
• ex 93 is read, nine cubed.

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3
2
3
2
7
3
3
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Lets Try a Few

• 42 4 ? 4 16
• 83 8 ? 8 ? 8 512
• 25 2 ? 2 ? 2 ? 2 ? 2 32

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Exponent Battle

• Use gt, lt or to determine who wins the battle.
• 42 vs. 24
• 83 vs. 38
• 25 vs. 63

lt
lt
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Extension Zero Power

• What do you think the value of 30 is?
• Lets see if we can find a pattern that will help
  us determine the answer using a different number
  such as 20...
• 21
• 22
• 23
• 24
• 25
• Will this pattern work for any base number to the
  power of zero?

As we work our way through the next exponent up
we simply multiply the previous answer by the
base number. If we wanted to work backwards we
would use the opposite of multiplication which is
division.
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Extension

• The opposite of addition is subtraction
• The opposite of multiplication is division
• The opposite of an exponent is its square root
• The symbol we use for a square root is _____. It
  is called the radical symbol
• For example we would read _____ as radical 9.
• When you see a number under the radical symbol it
  simply ask yourself, what number times itself is
  equal to that number?
• Not every number will have a perfect square root.
  A perfect square root occurs only when you have
  an answer that is a whole number.

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Extension

• The opposite of addition is subtraction
• The opposite of multiplication is division
• The opposite of an exponent is its square root
• The symbol we use for a square root is _____. It
  is called the radical symbol
• For example we would read _____ as radical 9.
• When you see a number under the radical symbol it
  simply ask yourself, what number times itself is
  equal to that number?
• Not every number will have a perfect square root.
  A perfect square root occurs only when you have
  an answer that is a whole number.

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Extension Square Roots

• How do you read ? Write your answer two
  different ways.
• 1)_______________________________________________
  ___
• 2)_______________________________________________
  ___
• What is the solution to the previous radical?
  _________
• How do you read ? Write your answer two
  different ways.
• 1)_______________________________________________
  ___
• 2)_______________________________________________
  ___
• What is the solution to the previous radical?
  _________
• How do you read ? Write your answer two
  different ways.
• 1)_______________________________________________
  ___
• 2)_______________________________________________
  ___
• What is the solution to the previous radical?
  _________

The square root of 25
Radical 25
5
The square root of 81
Radical 81
9
The square root of 75
Radical 75
Not a perfect square