Laws of Exponents

1
Laws of Exponents
2
Exponential Notation

• BaseExponent
• Base raised to an exponent

3
Goal

• To write simplified statements that contain
  distinct bases, one whole number in the numerator
  and one in the denominator, and no negative
  exponents.
• Ex

4
Description of Lesson

• This power point will address the laws of
  exponents in the following manner
• Explore how the rule works.
• State the rule.
• Provide an example with a solution.
• Provide extra examples (Find me to get solutions)

5
Exploration

• Evaluate the following without a calculator
• 34
• 33
• 32
• 31
• Describe a pattern and find the answer for
• 30

81
3
27
3
9
3
3
3
1
6
Zero Power
1
a0
Anything to the zero power is one
Can a equal zero?
No. You cant divide by 0.
7
Exploration

• Simplify

8
Product of a Power
If you multiply powers having the same base, add
the exponents.
9
Example
Simplify
10
Practice

• Simplify the following expressions

11
Exploration

• Simplify

12
Power of a Power
To find a power of a power, multiply the
exponents.
13
Example

• Simplify

14
Practice

• Simplify the following expressions

15
Exploration

• Simplify

16
Power of a Product
If a base has a product, raise each factor to the
power
17
Example

• Simplify

18
Practice
Simplify the following expressions
19
Negative Powers
A simplified expression has no negative exponents.
20
Example

• Simplify

21
Example

• Simplify

22
Practice

• Simplify the following expressions

23
Exploration

• Simplify

24
Quotient of a Power
To find a quotient of a power, subtract the
bottom exponent from the top if the bases are the
same.
25
Example

• Simplify

26
Practice
Simplify the following expressions
27
Exploration

• Simplify

28
Power of a Quotient
To find a power of a quotient, raise the
denominator and numerator to the same power.
29
Example

• Simplify

30
Practice
Simplify the following expressions