rational exponents math 017 intermediate algebra s. rook
TRANSCRIPT
Rational Exponents
MATH 017
Intermediate Algebra
S. Rook
2
Overview
• Section 7.2 in the textbook– Simplify rational exponents– Apply rational exponents to simplify rational
expressions
Simplify Rational Exponents
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Rational Exponents
• Thus far, we have only seen integer exponents– Ex: 53, x-5
• Possible to have rational (i.e. fractional) exponents– Ex: 81/3, y-3/4
5
Rational Exponents vs Radical Notation
• Relationship between rational exponents and radical notation
where p is power and r is radical
Ex:
• Most calculators take only up to the third root– How would we evaluate
prrp xx
24441
221
4 625
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Rational Exponents vs Radical Notation (Example)
Ex 1: Use radical notation to write the following and simplify if possible
51204183121 ,16,64,16 xx
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Rational Exponents vs Radical Notation (Example)
Ex 2: Use radical notation to write the following and simplify if possible
232343423 ,8,8,4 x
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Negative Rational Exponents
• Write any negative rational exponents as positive rational exponents
• Apply radical notation and simplify if possible
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Rational Exponents vs Radical Notation (Example)
Ex 3: Use radical notation to write the following and simplify if possible. Leave NO negative exponents
533245 32,8,16
Simplify Rational Exponent Expressions
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Simplify Rational Exponent Expressions
• Exponent rules for integer exponents apply to rational exponents as well– Remember them?
• Product: xa ∙ xb = xa+b • Quotient: xa / xb = xa-b • Power: (xa)b = xab
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Simplify Rational Exponent Expressions (Example)
Ex 4: Use the properties of exponents to simplify – write with only positive exponents
2321 cc
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Simplify Rational Exponent Expressions (Example)
Ex 5: Use the properties of exponents to simplify – write with only positive exponents
43
47
r
r
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Simplify Rational Exponent Expressions (Example)
Ex 6: Use the properties of exponents to simplify – write with only positive exponents
ts
ts2
23132
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Simplify Rational Exponent Expressions (Example)
Ex 7: Use the properties of exponents to simplify – write with only positive exponents
34121 32 xxx
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Simplify Rational Exponent Expressions (Example)
Ex 8: Use rational exponents to simplify the following – leave the final answer in radical notation
6 545 2 , wwyy
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Summary
• After studying these slides, you should know how to do the following:– Understand rational exponents. This includes
being able to convert to radical notation and simplify
– Simplify expressions containing rational expressions using the exponent rules