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Rational Exponents
Notes for R.6 Rational Exponents (pp. 55 – 62)
Topics: Negative and Rational Exponents and Their
Properties
I. Negative Exponents and the Quotient Rule (pp.55 – 57)
Recall: The Product Rule for Exponents states that
________
_____________
So the definition of a negative exponent is that we use
the reciprocal of the
____________________________.
*Negative exponents are instructions to rewrite as the reciprocal, not anything
left of
zero on the number line .
When we use the Quotient Rule and divide with exponents, we ___________________
_________________________________________________
Special cases:
a^{0} =1 and
II. Rational Exponents (pp. 58 –61)
Def., when n is an even positive integer, and when
a is positive. Also,
is called the _______________ n^{th} root of a.
Def., when n is an odd positive integer, and
when a is any real number . The
answer is the positive or the negative real number whose n^{th} power is a.
*Note the big difference that the ( ) make in the
solutions to these two problems!
For rational exponents with a value other than 1 in the numerator of its
exponent, then
or ,
whichever is more convenient.
or
Summary of Exponential Definitions and Rules
Factoring Polynomials with Rational Exponents: Factor out the smaller exponent.
III. Omit More Complex Fractions (p.61) (Stop video at
18:24 – 19:45)
IV. Calculator Notes :
• When entering an exponent in the calculator, use the ^ key or the “to the”
key.
Ex. 2^{3} is entered as “2 ^ 3” and read aloud as “Two to the third power”.
• When entering an exponent that is a fraction, you must use ( ) around the
fraction. Ex. is entered as “2 ^ ( 3 / 4 )”
Assignments: Text: pp. 62 – 63, #1 – 27 odd, 37 – 59 odd, 65, 73, 75 “A Review of Algebra ”: p. 175 #1, 3, 5 – 51 every other odd 
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