1. Exponents and Rules for Exponents Standard Form Factored Form Exponential Form 1=2 0 2=2=2 1 4 =2. 2 =2 2 8 =2. 2. 2 =2 3 16 =2. 2. 2. 2 =2 4

2. Exponents: Definition : a m = a. a. a. a. a… “m” number of times base exponent/power Multiply the base times itself “m” times. (0,1) y=b x

3. a = a 1 or 1a 1 = a If no exponent or coefficient – it is understood to be one. Exponent Rule Power of 1 Any number raised to the first power is equal to the number.

4. Any nonzero number raised to the zero power is 1. a 0 = 1 Exponent Rule Power of 0

5. A negative exponent means to take the reciprocal of that number, then raise it to the indicated power. Exponent Rule Negative Powers

6. A negative exponent means to take the reciprocal of that number, then raise it to the indicated power. For example, 5 -2 is telling you to take the reciprocal of 52 52 ( ), then square the 5( ). = **Short cut: If a negative exponent, move the base and exponent from the numerator to the denominator or vice versa. Example:

7. Examples: Zero & Negative Exponents 1.5 0 2.-3 0 3.(-6) 0 4. 5 x 10 0 5. 3 -2 6. 7. -3x 0 8. -x 0 9. (-4x) 0 10. 3x 0 + 4x 0 11. (3x) 0 + (4x) 0 12. -2xy 0 13. -14,285.7 0 = 1 = -1 = 1 =5 = -3 = -1 = 1 = 7 =2 = -2x = -1

8. More Examples: Zero & Negative Exponents 13. 5ac -5 14. 15. 16.

9. Graphing Under a Restricted Domain When graphing under a restricted domain, you will be given an interval of x values (domain). When graphing, only use values within this interval. This will also restrict the y values (range). You will graph only a part of the exponential function’s graph. No arrows on the graph to show that it continues. For example, graph y = 2 x under the domain {-3 < x < 3}.

10. Graphing Under a Restricted Domain (cont) Graph these points and connect them. x y -30.125 -20.25 -10.5 0 1 1 2 2 4 3 8 Domain: {-3 < x < 3} Range: {.125 < y < 8} {-3 < x < 3} {.125 < y < 8}

11. The End