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6.4 Rational Exponents

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

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  1. 6.4 Rational Exponents Algebra 2 Mrs. Spitz Spring 2007 SLIDE NUMBER #1

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. Ex. 1: Evaluate Method 1: Method 2: SLIDE NUMBER #7

  8. Ex. 2: Evaluate Method 1: SLIDE NUMBER #8

  9. Ex. 2: Evaluate Method 2: SLIDE NUMBER #9

  10. 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

  11. 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

  12. Ex. 3: Evaluate Method 1: Method 2: SLIDE NUMBER #12

  13. Ex. 4: Evaluate Method 1: SLIDE NUMBER #13

  14. Ex. 4: Evaluate Method 1: SLIDE NUMBER #14

  15. 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

  16. 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

  17. 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

  18. Ex. 7: Express in simplest radical form. SLIDE NUMBER #18

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