Using Properties of Exponents

1
Using Properties of Exponents
Tuesday, November 26, 2013

• EQ How do we use properties of exponents?

M2 Unit 5a Day 1
2
Properties of Exponents Let a and b be real
numbers and let m and n be integers. Product of
Powers Property Power of a Power Property Power
of a Product Property Zero Exponent
Property Quotient of Powers Property Power of
Quotient Property Negative Exponent Property
3
Product of Powers
To multiply powers with the same base, add the
exponents and keep the common base.

• Examples
• a.
• b.

4
Your turn 1. 2. 3.
Keep common bases
Add the exponents
5
Power of a Power
To raise a power to a power, keep the base and
multiply the exponents.

• Examples
• a.
• b.

6
Your turn 1. 2. 3.
Keep The Base

Multiply The Exponents
7
Power of a Product
To raise a product to a power, raise each factor
to the power.

• Examples
• a.
• b.

Simplify any numeric bases raised to exponents
This should remind you of the distributive
property. Remember to distribute the exponent
to each base, numeric and variable!
Warning No distributing over addition!!!
8
Your turn 1. 2. 3.
Raise Each Factor To The Power
Its Like The Distributive Property
9
Zero Exponent
Any number raised to the zero power is equal to
1.

• Examples
• a.
• b.

10
Your turn 1. 2. 3.
Anything Raised To The Zero Power
1
11
Quotient of Powers
To divide powers with the same base, subtract
the exponents and keep the common base. Also,
remember that common factors cancel out!

• Examples
• a.
• b.

Keep the base where the exponent is larger
12
Your turn 1. 2. 3.
Common Factors Cancel Out
With Common Bases Subtract Exponents
13
Power of Quotient
To raise a quotient to a power, raise the
numerator and the denominator to the power.

• Examples
• a.
• b.

14
Raise the numerator and denominator to the power
Your turn 1. 2. 3.
Simplify any factors with numeric bases
15
Negative Exponent Property

• You may want to think of it this way unhappy
  ( ) exponents will
  become happy ( ) by having the
  base/exponent pair switch floors!
• Example
• A.) B.)

positive
negative
16
You try

• 1.
• 2.
• 3.
• 4.

17
Simplifying Exponential Expressions

• To simplify exponential expressions completely
• Get rid of parentheses
• Get rid of negative exponents
• Make sure there is only one of each base
• Cancel out common factors

18
Simplify the exponential expression.
multistep

• Examples
• A.

• B.

C.

• D.

19
You try
multistep
1.
2.
3.
4.
20
multistep
Simplify the exponential expression.

• A.
• B.
• C.
• D.

21
You Try5.6. 7.
multistep