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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:

a0 =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 _______________ nth 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 nth 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.


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. 23 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 )”

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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