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An explanation of the Product to a Power and Quotient to a Power rules for exponents. It includes examples and instructions for simplifying expressions. The document also mentions the absence of Sum to a Power and Difference to a Power rules.
What you will learn
Typology: Exercises
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Exponential Notation:
𝑛
base and 𝑛 is the exponent
exponential notation represents the product of repeated factors (the
base times itself some number of times)
o anytime you have an exponent that is a positive integer you can
write the base that number of times
o another option is to use the rules we’ve covered so far (Product,
Quotient, and Power), or the rules we’re about to cover (Product
to a Power and Quotient to a Power)
Product to a Power Rule:
each factor (don’t forget the coefficients)
o
4
3
2
2
5
3
Example 1: Simplify each expression COMPLETELY.
a. − 9 𝑦
3
3
2
b. (
− 6
𝑦
2
𝑦
4
3
3
b.
For help using the
TI-30Xa calculator,
take a look at the
Calculator Tips
document in
Brightspace.
Example 2 : Simplify each expression COMPLETELY. Do NOT leave
negative exponents in your answers.
a. − 8 𝑦
2
3
4
b.
2
5
2
b.
c. (
1
2
4
6
5
d. (
2 𝑥
4
𝑦
7
3
−𝑥
5
2 𝑦
6
2
d.
8 𝑥
12
𝑦
21
𝑥
10
4 𝑦
12
8 𝑥
22
4 𝑦
33
𝟐𝒙
𝟐𝟐
𝒚
𝟑𝟑
e. (−
3
2
4
9
2
16
f. − (
5
4
3
1
2
6
125
64
1
64
125
64
1
64
124
64
𝟑𝟏
𝟏𝟔