Bell Work: Evaluate each expression: (-2)3 3. (1/2)3

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Presentation transcript:

Bell Work: Evaluate each expression: 1. 42 2. (-2)3 3. (1/2)3 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 Goal: I can evaluate powers that have zero and negative exponents.

Looking for a Pattern Copy the table. Use the patterns to complete the table. Write non-integers as fractions in simplest form. Exponent, n 3 2 1 -1 -2 -3 Power 2n 8 4 ? Power 3n 27 9 Power 4n 64 16

Zero and Negative Exponents Zero and negative exponents are too easy. DEFINITION OF NEGATIVE EXPONENTS a-n is the reciprocal of an. , where a is not equal to 0. 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!

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! Important – only move the base number and the negative exponent that goes with it!

Examples a. 3-4 = b. 4-y = c. d. 0-1 =

Zero and Negative Exponents Zero and negative exponents are too easy. DEFINITION OF ZERO EXPONENTS A nonzero number to the zero power has the value of ONE. ANY NUMBER (except zero!) RAISED TO THE ZERO POWER IS ONE!!!! a0 = 1, where a is not equal to 0. 970 = 1 50 = 1 1000 = 1 -40 = 1 80 = 1 7650 = 1 3000 = 1 -220 = 1 -90 = 1 19870 = 1 1,000,0000 = 1 22.8790 = 1 1,5670 = 1

More Examples – Rewrite with positive exponents. Assume k is positive. a. 4(3-k) = b.

More Examples – Evaluate the Expression b. (5-2)-3 = c. 2-3 =

Examples – Rewrite with positive exponents. Assume n is positive. a. (4y)-3 = b.

How do you graph an exponential function? To sketch the graph of y = 2x, make a table of values that includes negative x values…… x -2 -1 1 2 3 2x Next, plot the points on a coordinate plane. What do you notice about the graph? Safety tips….. Use integer values for x. Base number should always be greater than zero (in this class). In real life applications, x is usally the time period.

Review Assignment: Page 459 14 - 48 even