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 4

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

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.

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

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

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 ( ), 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:

Examples: Zero & Negative Exponents (-6) x x x 0 9. (-4x) x 0 + 4x (3x) 0 + (4x) xy , = 1 = -1 = 1 =5 = -3 = -1 = 1 = 7 =2 = -2x = -1

More Examples: Zero & Negative Exponents 13. 5ac

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}.

Graphing Under a Restricted Domain (cont) Graph these points and connect them. x y Domain: {-3 < x < 3} Range: {.125 < y < 8} {-3 < x < 3} {.125 < y < 8}

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