Download Chapter 7.2(a and b) Rational Exponents.notebook

Chapter 7.2(a and b) Rational Exponents.notebook
March 30, 2017
Bellwork:
Homework Questions???
Solve by factoring:
1) x2 + x = 72
2) 3x2 = ­11x ­ 10
3) Write the equation of the line parallel to x = ­2 that passes through the point (6, 12).
Simplify:
4)
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Chapter 7.2(a) Rational Exponents
Understand the meaning and use , , and to simplify rational exponents.
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Definition of If n is a positive integer greater then 1 and is a real number, then
1) Use Radical notation to write the following. Simplify if possible.
a. b.
c.
d.
e.
f.
example: b > 1, suppose Mar 24­8:07 AM
Mar 24­9:43 AM
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Chapter 7.2(a and b) Rational Exponents.notebook
2) Use Radical notation to write the following. Simplify if possible.
a. b.
c.
d.
March 30, 2017
Definition of If m and n are positive integers greater than 1 with
lowest terms, then in as long as is a real number.
The denominator n of the rational exponent corresponds to the index of the radical.
e.
f.
The numerator m of the rational exponent indicates that the base is to be rasied to the mth power.
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3) Use radical notation to write the following. Then simplify if possible.
Note: You can raise the base to the exponent and then take the nth root or you can find the root and then raise it the mth power. Typically a.
b.
c.
d.
is easier to calculate. e
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4) Use radical notation to write the following. Then simplify if possible.
a.
b.
Take a Short Break
c.
d.
e
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Chapter 7.2(a and b) Rational Exponents.notebook
March 30, 2017
Definition of Which of the following is correct?
as long as is a nonzero real number.
4) Write each expression with a positive exponent, and then simplify.
a.
b.
c.
d.
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Review Exponent Rules
Exponent Rules
If m and n are rational numbers, and a, b and c are numbers for which the expressions below exist, then
Chapter 7.2(b) Rational Exponents
Product Rule
Be able to use rules for exponents to simplify expressions that contain rational exponents.
Power Rule
Power Rules Products and Quotients
c ≠ 0
Quotient Rule
a ≠ 0
Zero Exponent
a ≠ 0
Negative Exponent
Note: For the remainder of the chapter, we will assume that variables represent positive real numbers.
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re
All the properties of exponents hold true for rational exponents as well as integer exponents.
1) Use the properties of exponents to simplify. Write results with only positive exponents.
a. b.
c.
d. Mar 27­1:04 PM
2) Use the properties of exponents to simplify. Write results with only positive exponents.
a. b.
c.
d. Mar 27­1:04 PM
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Chapter 7.2(a and b) Rational Exponents.notebook
March 30, 2017
3) Use the properties of exponents to simplify. Write results with only positive exponents.
Homework
P. 426­427 #1­59 (odds)
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