Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
8.2- Zero and Negative Exponents Bell Work: Evaluate each expression: 1. 42 2. (-2)3 3. (1/2)3 4. 2 * 1.053 5. 34 * 33 Answers: 1. 16 2. -8 3. 1/8 4. 2.205 5. 2187 8.2 Zero and Negative Exponents I can evaluate powers that have zero and negative exponents. Zero and Negative Exponents Let ‘n’ be a positive integer and ‘a’ be a nonzero number. Negative Exponents a n 1 n a reciprocals 2 3 1 1 2 3 9 Zero Exponents a 1 0 5 1 0 A nonzero number to the zero power has the value of ONE. ANY NUMBER (except zero!) RAISED TO THE ZERO POWER IS ONE!!!! Example What this really means is that you turn a negative exponent into a positive exponent by shifting the power from numerator to denominator or vice versa! 1 1 2 2 2 4 2 1 1 4 3 4 64 3 Important – only move the base number and the negative exponent that goes with it! Evaluate the expressions. 1) 3) 4 3 1 3 1 1 3 4 64 2 1 1 3 1 1 9 9 2 2) 0 4) 9 0 1 9 0 (5) 1 Simplify expressions: write with positive exponents. (-5)-3 = 1 = -1 (-5)3 125 244-3 = 24 ∙ 1 = 24∙ 1 = 3 43 -3-4 = 1 = - 1 4 -3 81 64 8 Simplify expressions: write with positive exponents. 3a-3b-2 = 33 2 ab (3-3)2= 3(-3 ∙ 2) = 3-6 = 1 1 = 6 3 729 Graphing with a variable as an exponent Sketch the graph of y = 2x x 2 1 2x 4 2 0 -1 20=1 2-1= ½ -2 2-2 = ¼ 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 1.0047t Where t = 0 for 1980 Find the population in 1970, 1980, and 1990 To find the population, plug the numbers into the formula and then use a calculator. Pop in 1970 t = -10 Pop in 1990 t = 10 Do you expect it to be more or less in 1970 than 1980? P = 4,903,000 1.0047-10 (set up the problem) = 4,678,406 (calculate) This is the population in 1970. Population in 1990: P = 4,903,000 1.004710 P = 5,138,376 Assignment 8.2 (pg. 459- 460) #14-50, #64 EVEN