Lesson Notes Section 1 - Purdue University
Lesson 8 Notes Sections 1.6
Rules of Exponents
A Product and Quotient Rules
Product Rule: [pic] 1. Keep Base
2. Add exponents
Quotient Rule: [pic] 1. Keep Base
2. Subtract exponents
(numerator - denominator)
Examples:
1) [pic]
2) [pic]
3) [pic]
4) [pic]
5) [pic] 6) [pic]
7) [pic]
Caution: [pic]
and [pic]
B Zero and Negative Exponent Rules
Zero Exponent: [pic]
Negative Exponent: [pic], [pic] [pic]
Examples:
1) [pic] 2) [pic]
3) [pic]
4) [pic]
5) [pic] 6) [pic]
7) [pic] 8) [pic]
9) [pic]
Caution: A negative number does not necessarily mean a negative number. Think reciprocal when you see a negative exponent, not negative number.
C Power Rules
[pic] [pic] [pic]
Note: Power Rules are used top remove or clear parentheses.
Examples:
1) [pic] 2) [pic]
3) [pic]
4) [pic]
5) [pic]
D Putting all the Rules together....
The rules can be performed in many different orders when simplifying expressions. However, if you do not know what order to use, these steps usually work well.
1. Simplify within parentheses first using product or quotient rules and/or negative or zero rules.
2. Clear parentheses by using power rules.
3. Change any zero or negative exponent rules.
4. Continue with product or quotient rules, if necessary.
5. Evaluate or simplify any numbers, if needed.
Examples:
1) [pic]
2) [pic]
3) [pic]
4) [pic]
-----------------------
Product Rule
Quotient Rule
................
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