6.4 Rational Exponents

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6.4 Rational Exponents. Algebra 2 Mrs. Spitz Spring 2007. Objectives. Write expressions with rational exponents in simplest radical form and vice versa, and Evaluate expressions in either exponential or radical form. Assignment.

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### 6.4 Rational Exponents

Algebra 2

Mrs. Spitz

Spring 2007

SLIDE NUMBER #1

Objectives
• Write expressions with rational exponents in simplest radical form and vice versa, and
• Evaluate expressions in either exponential or radical form.

SLIDE NUMBER #2

Assignment
• Pp. 272-273 #4-66 every 3rd problem. If you need practice, then work on other problems.
• You will have a quiz on Friday, so you need to review over these on Thursday.

SLIDE NUMBER #3

Application
• Nina deposited \$500 in her account at First Atlanta Bank on March 1. Her account earns 8% interest per year. If she withdraws the money to pay for her college tuition at the beginning of September, how much interest has she earned? The bank uses the formula A=P(1 + r)t for finding the amount of money (A) in a compound interest account at the end of t years if P is the original amount of money deposited and r is the annual interest rate. A=P(1 + r)½

SLIDE NUMBER #4

Application
• Nina had her money in the bank for 6 months. But, t is expressed in years, so substituting ½ for t, we must evaluate A= 500(1 + 0.08)½ to find the amount of interest she earned. But how do we evaluate a fractional exponent? Assume that fractional exponents behave as integral exponents. Then 51 = 5(1/2)2 or (51/2)2.
• So, 51/2 is number that when squared equals 5. Since you know that (5)2 also equals 5, then 51/2 = 5).

SLIDE NUMBER #5

Definition of

For any real number b and for any integer, n, n > 1,

From the definition, we can say that and that

or -2. The expression is not defined since -16 < 0 and 4 is even. Can you tell why this restriction is needed?

Except when b < 0 and n is even.

The number is not defined and it is not real.

SLIDE NUMBER #6

Ex. 1: Evaluate

Method 1:

Method 2:

SLIDE NUMBER #7

Ex. 2: Evaluate

Method 1:

SLIDE NUMBER #8

Ex. 2: Evaluate

Method 2:

SLIDE NUMBER #9

What if the fractional exponent in the numerator isn’t 1?
• How can you evaluate an expression with a fractional exponent in which the numerator is not 1? Study on children.
• Method 1:

Method 2:

have the same value.

SLIDE NUMBER #10

Definition of Rational Exponents
• For any nonzero real number b, and any integers m and n, with n > 1,

except when b < 0 and n is even.

SLIDE NUMBER #11

Ex. 3: Evaluate

Method 1:

Method 2:

SLIDE NUMBER #12

Ex. 4: Evaluate

Method 1:

SLIDE NUMBER #13

Ex. 4: Evaluate

Method 1:

SLIDE NUMBER #14

Decimal Numbers?
• As you may know, fractions are rational numbers that can also be written as decimal numbers. For examples 2/3 = 0.6 and ¾ = 0.75. We can use a calculator to evaluate expressions with fractional or decimal exponents.

SLIDE NUMBER #15

Ex. 5: Use a calculator to evaluate

ENTER 1331

yn

(

2

3

)

=

121

To evaluate an expression with a decimal exponent, enter the decimal after the key. When simplifying, a radical, find the smallest index possible.

yn

SLIDE NUMBER #16

Ex. 6: Find in simplest radical form.

In , the index is 6. Methods 1 and 2 both illustrate using a smaller index.

Method 1:

Method 2:

SLIDE NUMBER #17

SLIDE NUMBER #18