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Exponent Rules Notes

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EXPONENT RULES
Exponent Definition:
Part A: Product Rule
1. Simplify 42•43
2. Simplify x2•x3
 Hint: Rewrite the terms in expanded form: x2 = ___________ and x3 = __________
 How many x’s are there?
 Rewrite your answer with exponents: _____________________________
3. Now simplify x4•x8
4. x?•x5 = x11

? = __________
Now look at your answers in Part A. What do you observe? Write a rule explaining what you did.
Part B: Power Rule
1. Simplify (43)2
2. Simplify (x3)2
 Hint: Rewrite the term in expanded form: x3 = ___________
 Now if we square it, what does that mean?
 (xxx)(xxx)
 Rewrite your answer with exponents: _____________________________
3. Now simplify (x8)5
4. (x?)5 = x30

? = __________
Now look at your answers in Part B. What do you observe? Write a rule explaining what you did.
EXPONENT RULES
Part C: Quotient Rule
𝑥3
1. Simplify 𝑥 5


Hint: Rewrite the terms in expanded form, and reduce common factors
How many x’s are left? Are they in the numerator or denominator?
 Rewrite your answer with exponents: _____________________________
2. What stays in the numerator if all the factors “cancel out”?
3. Simplify
4. Simplify

𝑥7
𝑥5
𝑥 11
𝑥?
= 𝑥2
? = __________
Now look at your answers in Part C. What do you observe? Write a rule explaining what you did.
Part D: Negative Exponents Rule
1. Simplify 3 − 7
 Is your answer positive or negative?
2. Look back at Part C, if you use the Division Rule to simplify
𝑥3
𝑥7
, is the x4 in the numerator or
denominator?
3. What does this tell you about negative exponents?
4. Simplify x-6 using only positive exponents
1
5. Simplify 𝑥 −7 using only positive exponents
Now look at your answers in Part D. What do you observe? Write a rule explaining what you did.
EXPONENT RULES
Part E: Parentheses: Distributing Exponents
THIS RULE ONLY WORKS IF THERE IS MULTIPLICATION OR DIVISION IN THE
PARENTHESES. If the parentheses contain addition or subtraction, DO NOT APPLY THIS RULE
1. Write (2𝑥)3 in expanded form: ____________________
2. Simplify the expression in #1: _______________________
𝑥 4
3. Write (5) in expanded form: ___________________
4. Simplify the expression in #3.
When there is a product or quotient in parentheses, you can _______________________ the exponent.
Part F: Zero Exponents
Anything raised to the zero power = _____
Use the following pattern to figure out the zero exponent rule:
23 =
22 =
21 =
20 =
2−1 =
2−2 =
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