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Chapter 7.2(a and b) Rational Exponents.notebook
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March 30, 2017
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Bellwork:
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) 5)
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Homework Questions???
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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
example: b > 1, suppose
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1) Use Radical notation to write the following. Simplify if possible.
a. b.
c. d.
e. f.
Chapter 7.2(a and b) Rational Exponents.notebook
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March 30, 2017
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2) Use Radical notation to write the following. Simplify if possible.
a. b.
c. d.
e. f.
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Definition of
If m and n are positive integers greater than 1 with in lowest terms, then
as long as is a real number.
The denominator n of the rational exponent corresponds to the index of the radical.
The numerator m of the rational exponent indicates that the base is to be rasied to the mth power.
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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 is easier to calculate.
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3) Use radical notation to write the following. Then simplify if possible.
a. b.
c. d.
e
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4) Use radical notation to write the following. Then simplify if possible.
a. b.
c. d.
e
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Take a Short Break
Chapter 7.2(a and b) Rational Exponents.notebook
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March 30, 2017
Mar 2410:07 AM
Definition of
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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Which of the following is correct?
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Chapter 7.2(b) Rational Exponents
Be able to use rules for exponents to simplify expressions that contain rational
exponents.
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Note: For the remainder of the chapter, we will assume that variables represent positive real numbers.
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
Product Rule
Power Rule
Power Rules Products and Quotients c ≠ 0
Quotient Rule a ≠ 0
Zero Exponent a ≠ 0
Negative Exponent
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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.
re
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2) Use the properties of exponents to simplify. Write results with only positive exponents.
a. b.
c. d.
Chapter 7.2(a and b) Rational Exponents.notebook
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March 30, 2017
Mar 271:04 PM
3) Use the properties of exponents to simplify. Write results with only positive exponents.
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Homework
P. 426427 #159 (odds)