1. 8.2 Negative and Zero Exponents I love exponents!

2. Definition of Negative Exponents (let a be a nonzero number and let n be a positive integer) The expression a -n is the reciprocal of a n. a -n = 1 a ≠ 0 a n 1 = a n a -n 3 -2 = 1 3232 = 1 9

3. The negative exponent says the number needs to be moved to the opposite location and made positive. If it’s negative in the numerator, it belongs in the denominator position positive. If it’s negative in the denominator position, it belongs in the numerator position positive.

4. Definition of Zero Exponent (let a be a nonzero number and let n be a positive integer) A nonzero number to the zero power is ALWAYS 1! a 0 = 1a  0 3 0 = 1 (x 2 y 5 ) 0 = 1 The expression 0 0 is undefined.

5. Simplify expressions: write with positive exponents. (-5) -3 = 24  4 -3 = -3 -4 = 1 (-5) 3 = - 1 125 24 ∙ 1 4 3 = 24∙ 1 = 3 64 8 1 -3 4 1 81 = -

6. Simplify expressions: write with positive exponents. 3a -3 b -2 = 3 a3b2a3b2 (3 -3 ) 2 =3 (-3 ∙ 2) = 3 -6 = 1 3636 = 1 729

7. Graphing with a variable as an exponent x3210-2-3 2x2x 8422 0 =12 -1 = ½2 -2 = ¼2 -3 = 1 / 8 Sketch the graph of y = 2 x Will it ever touch the x-axis?

8. Example: (Just follow this example to see what you get to do on your assignment.) Between 1970 and 1990, the Missouri population increased at a rate of.47% per year. The population P in t years is given by: P = 4,903,000  1.0047 t Where t = 0 for 1980

9. To find the population, plug the numbers into the formula and then use a calculator. Find the population in 1970, 1980, and 1990 Pop in 1970t = -10 Pop in 1990t = 10 P = 4,903,000  1.0047 -10 (set up the problem) = 4,678,406(calculate) This is the population in 1970. Do you expect it to be more or less in 1970 than 1980?

10. Population in 1990: P = 4,903,000  1.0047 10 P = 5,138,376