Exponent Properties: The Product Rule
1. What is the difference between 3x and x3? Explain in complete sentences and with examples.
2. Exponential expressions multiplied with each other that have the same base.
Product
Repeated Multiplication
Power of the form ab
22 (23)
2*2*2*2*2
25
34 (35)
116 (118)
51 * 54 * 53
X3 * X4
3. Now, explain a general rule for what happens when we have two exponential expressions
multiplying each other with the same bases. You can write the rule in words, or use an example
or expression to communicate the rule.
4. Why do you think this rule is called the product rule?
5. Write the algebraic rule for this concept.
http://www.scribd.com/doc/79685847/Exponent-Rules-Proof-Worksheets
Exponent Properties: The Distributive Rule for Products
1. What does it mean to “distribute”?
Product
Repeated
Multiplication
(2 * 3)3
(2*3) (2*3) (2*3)
Rearrange the
multiplications using the
commutative property, so
similar things are next to
each other.
2 *2*2*3*3*3
Power of the form
ac * bc
2333
(4*6)4
(x*y)5
(3*4*5)2
(3x)6
2. Now, explain a general rule for what happens when we have two exponential expressions
multiplying each other with the same bases. You can write the rule in words, or use an example
or expression to communicate the rule.
3. Why do you think this rule is called the distributive rule?
4. How is this rule different from the product rule?
5. Write the algebraic rule for this concept.
http://www.scribd.com/doc/79685847/Exponent-Rules-Proof-Worksheets
Exponent Properties: The Quotient Rule
1. What does the term “quotient” mean?
Quotient
Repeated Multiplication
Cancel out
Power of the form
Ab
23
22
2*2*2
2*2
2*2*2
2*2
21
37
34
X10
X4
512y20
57y8
Too big to write out? Find another way!
A7b3
2. Now, explain a general rule for what happens when we have two exponential expressions
dividing each other with the same base. You can write the rule in words, or use an example or
expression to communicate the rule.
3. Write the algebraic rule for this concept.
http://www.scribd.com/doc/79685847/Exponent-Rules-Proof-Worksheets
Exponent Properties: The Zero Exponent Rule
1. Why does a zero exponent result in an answer of “1”?
Quotient
Use the quotient rule to write in
the form ab
Look at the original quotient.
What is the result as just a
number?
23
23
57
57
X20
X20
2. What do you think any rational number to the zero power should equal? Write an expression
to demonstrate your answer.
http://www.scribd.com/doc/79685847/Exponent-Rules-Proof-Worksheets
Exponent Properties: The Distributive Rule for Quotients
1.
Quotient
Repeated Multiplication
Write as a fraction
2. Now, determine a general rule for what happens when we have a quotient raised to a
power. You may want to write the rule in words, or you can use an example or expression to
communicate the rule.
3. Why is this rule called the distributive rule for exponents?
4. Write the algebraic rule for this concept.
http://www.scribd.com/doc/79685847/Exponent-Rules-Proof-Worksheets
Exponent Properties: The Power Rule
1. What information have you already learned that helps explain a power to a power?
Problem to simplify
First repeated
multiplication
Second repeated
multiplication
Power of the form
Ac
(22)2
22 * 22
2*2*2*2
24
(53)4
X6 * x6 * x6 * x6
712
(35y2)3
(a20)32
Too big to write out? Find another way
2. Now, determine a general rule for what happens when we have something already to a power,
raised to a power again. You may want to write the rule in words, or you can use an example or
expression to communicate the rule. How is this rule different from the product rule?
3. How is this rule different from the product rule?
4. Write the algebraic rule for this concept.
http://www.scribd.com/doc/79685847/Exponent-Rules-Proof-Worksheets
Exponent Properties: Negative Exponents
1.
Quotient
Repeated Multiplication
Answer as a fraction
22
25
a4
a9
___2 * 2__
2*2*2*2*2
1
23
Use the quotient rule
to get power of the
form ac
22-5 = 2-3
1
48
x*x*x*y
x*x*x*x*x*x*x
a4b5
a9b12
50
254
2. What does a negative exponent mean? Look at the two columns on the right and try to
formulate a rule.
3. Are positive expressions with negative exponents negative?
4. What do you think this simplifies to be?
mathematically.
1_ Go ahead and take a guess or try to work it out
2-3
5. Write the algebraic rule for this concept.
http://www.scribd.com/doc/79685847/Exponent-Rules-Proof-Worksheets