# 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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