1. Properties of Exponents
Common Pitfalls

2. Properties of Exponents
Addition
Must be like terms.
Add coefficients, keep the exponent the same.
Multiplication
Can be unlike terms (but still same letter).
Multiply coefficients, add the exponents.

3. Properties of Exponents
Product Rule
To combine two powers (with the same base) into one, add the exponents.
Combine = Add
Power Rule
To raise a power to another exponent separated by parenthesis, multiply.
Parenthesis = Multiply
add
multiply
to combine
parenthesis

4. Properties of Exponents
Power of a Product Rule
If n is a positive integer and a and b are real numbers, then
Power of a Quotient Rule
If n is a positive integer and a and b are real numbers and b≠0, then
Don’t do it!
NO!
There is no power of a sum rule!
We will learn how to deal with this in Section 13.5.

5. Properties of Exponents
Negative Base
Negative Exponent
Negative exponent = reciprocate.
Does not change the sign of the base.