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
Copyright © Lynda Greene Aguirre 2009 1 Exponential Form is used when you want to multiply the same number by itself several times. The “base” is the actual number we will multiply 5 4 The “power” is how many bases will be multiplied. Read as: Five to the Fourth power 5 is the base 4 is the power (also called the exponent) Copyright © Lynda Greene Aguirre 2009 2 Definitions: 5 x 5 x 5 x 5 is called EXPANDED NOTATION 5 4 is called EXPONENTIAL NOTATION Copyright © Lynda Greene Aguirre 2009 3 For example: 5 4 five to the fourth power means to perform this multiplication: 5 x 5 x 5 x 5, (multiply four 5’s together). 5 x 5 x 5 x 5 = 625 Answer Copyright © Lynda Greene Aguirre 2009 4 Using a Calculator to evaluate exponents Calculators use different buttons, but the most common one is this one ^ . 4 A problem like 3 (four to the third power) Means 4 x 4 x 4 = 64 Enter it in the calculator as: 4 ^ 3 = 64 Copyright © Lynda Greene Aguirre 2009 5 Using your calculator, evaluate the following exponents: 12 22 32 42 52 62 72 82 9 10 2 11 12 132 14 2 15 2 2 Copyright © Lynda Greene Aguirre 2009 2 2 6 Exponent Expansion Write in Expanded Form, then evaluate (if possible) 7 Exponent Rules Rule: 8 Exponent Rules: double powers Notice that you can get the same answer by multiplying the powers Rule: 9 Exponent Rules Expand and evaluate each problem below You can cancel the same number (top and bottom)as long as it’s multiplication Need to put a “1” on the bottom if all the numbers are wiped out in the cancelling step Need to put a “1” on top if all the numbers are wiped out in the cancelling step Notice that you can get to the same answer by subtracting the powers (top-bottom) Rule: 10 Copyright © Lynda Greene Aguirre 2009 11 The Exponent, or power, indicates how many bases should be multiplied. When the power is a zero, that means that there are no bases. The “power” indicates that there will be no 3’s 0 3 Copyright © Lynda Greene Aguirre 2009 Read as: Three to the zero’th power 12 However, this is not equal to zero, it is defined as: 3 1 0 Definition of a Zero Exponent: Anything raised to the zero’th power is equal to “1” It doesn’t matter what is being raised the power of zero, it will be equal to the number “1”. Copyright © Lynda Greene Aguirre 2009 x 1 0 (5 x) 0 1 ( x 3 y 6) 0 1 13 Copyright © Lynda Greene Aguirre 2009 14 Negative Exponents First write the base as a fraction (if it’s not already written that way) Move the 4’s to the bottom and tear up the parking ticket Parking Ticket: The negative power means that the base (the “4” in this case) is in the wrong place. Since this is a fraction, there are only two “parking places”, the top or the bottom. (i.e. change the negative power into a positive power) Finish the problem Copyright © Lynda Greene Aguirre 2009 15 Practice Problems 7x 5x 2 2 3 3 0 2 42 x 0 63 81 x 2 Copyright © Lynda Greene Aguirre 2009 4 50 2 4 x 3 1 2 2 y 16