Exponents

1
Exponents
2
Review

• Evaluate each expression
• 3³
• 7¹
• -6²
• (?)³
• (-6)²
• 3 2³

• Answers
• 27
• 7
• -36
• 27/512
• 36
• 24

3
Definitions

• Exponential Expression 5?
• 5? 5(5)(5)(5)(5)(5)(5)(5)(5)
• Base the repeated factor of an exponential
  factor
• Exponent number of times that the base is used
  as a factor
• POWER

4
Review

• Evaluate the expression by substituting the
  number in for the variable
• X -3 y 4 z -1
• 2x²y _________
• Answer 2(-3)²(4) 72

• 9
• Z²x
• 9
• (-1)²(-3)
• 9/(-3) -3

5

• What does x³?
• X³ (x)(x)(x)

6
Product Rule for Exponents

• If m and n are positive integers, and b is a real
  number, then..
• Example
• 3³ 34 37
• Why?
• (333) (3333) 37

7
Examples

1. 4³ 4
2. (-3)² (-3)7
3. x³ x x²
4. 3x³ 4x²
5. (3y4)(-10x7)(4xy³)

• 44
• (-3)?
• x6
• (3 4) (x³ x²) 12x5
• (3 -10 4)(y4 y³)(x7 x)
• -120y7x8

8
Helpful Hint p. 299

• Multiplication
• 5x² 4x² 20x4
• 6x³ 7x² 42x5

• Addition
• 5x² 4x² 9x²
• 6x³ 7x²
• Cannot simplify! Not like terms!

9
Lets think about it!

• (x²)³
• (x²)(x²)(x²)
• x6

10
Shortcut Power Rule for Exponents

• If m and n are positive integers, and b is a real
  number, then.
• Example
• (y4)²
• y8

11
Practice

• (96)8
• (x?)7

• Think about it
• (2x5y4)³
• Remember
• (2x5y4)(2x5y4)(2x5y4)
• (2 2 2)(x5 x5 x5)(y4 y4 y4)

12
Short Cut Power of a Product Rule

• If n is a positive integer and a and b are real
  numbers, then..
• Examples
• 1). (3y)4 2). (-2g²hj³)4

13
Power of a Quotient Rule

• If m is a positive integer and b and c are real
  numbers, then..

14
Example
15
Think of your own rule Simplify each one
16
Quotient Rule for Exponents

• If m and n are positive integers, and b is a real
  number, then..

17
Why are these two the same?

• x4
• x4

• 5
• 5

18
Zero Exponent Rule

• If a is a real number, then
• As long as a is not zero!

19
Practice

1. x
2. 7
3. (-3)
4. -3
5. x5y

1. 1
2. 1
3. 1
4. -1
5. x5