1. Summer Assignment Review
Exponent Rules

2. Properties of Exponents
Product of Powers Property
Let a be a real number, and let m and n be positive integers.
To multiply powers having the same base, add the exponents.
Examples
**Each individual property is simple. The difficulty is keeping them straight once you have learned them all, and in remembering that the operation you perform on the exponents is not the operation that is occurring between the powers.

3. Properties of Exponents
To multiply monomials, re-order the factors in order to multiply powers with like bases.
I call this a training wheel step. This work can be done in your head, or by drawing arrows between the like bases on the original problem.
Examples

4. Properties of Exponents
Power of a Power Property
Let a be a real number, and let m and n be positive integers.
To raise a power to a power, multiply the exponents.
Examples
This property is often confused with the product of powers property. Because of this you need to pay close attention to these two. Look at how they are related.

5. Properties of Exponents
Power of a Product Property
Let a be a real number, and let m and n be positive integers.
To find a power of a product, find the power of each factor.
Examples
When applying all three of these rules there are multiple paths to a simplified expression.
Be careful, don’t multiply the constant by the power!

6. Properties of Exponents
Practice
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7. Properties of Exponents
Quotient of Powers Property
Let a be a nonzero real number, and let m and n be positive integers such that m > n
To divide powers having the same base, subtract the exponents
We are actually cancelling out matching factor pairs…
Subtracting accomplishes the same goal with out all that work.

8. Properties of Exponents
Power of a Quotient Property
Let a and b be a real numbers with b≠0, and let m be a positive integer.
To find a power of a quotient, find the power of the numerator and the power of the denominator and divide.
Basic Examples:
Using more than one property:
Training wheels step

9. Properties of Exponents
Practice
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10. Properties of Exponents
Zero Exponents
Negative Exponents
a to the power of zero is 1.
A simplified expression can not contain any negative exponents

11. Properties of Exponents
Practice