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3. Exponential Form is used when you want to multiply the same number by itself several times. 5 is the base 4 is the power (also called the exponent) The “base” is the actual number we will multiply The “power” is how many bases will be multiplied. Read as: Five to the Fourth power 2

4. Copyright © Lynda Greene Aguirre 2009 Definitions: 5 x 5 x 5 x 5 is called EXPANDED NOTATION is called EXPONENTIAL NOTATION 3

5. Copyright © Lynda Greene Aguirre 2009 For example: 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 4

6. Using a Calculator to evaluate exponents Calculators use different buttons, but the most common one is this one ^. Copyright © Lynda Greene Aguirre 2009 Means 4 x 4 x 4 = 64 Enter it in the calculator as: 4 ^ 3 = 64 A problem like (four to the third power) 5

7. Using your calculator, evaluate the following exponents: Copyright © Lynda Greene Aguirre 2009 6

8. 7 Exponent Expansion Write in Expanded Form, then evaluate (if possible)

9. 8 Rule: Exponent Rules

10. 9 Exponent Rules: double powers Rule: Notice that you can get the same answer by multiplying the powers

11. 10 Rule: Exponent Rules You can cancel the same number (top and bottom)as long as it’s multiplication Need to put a “1” on top if all the numbers are wiped out in the cancelling step Need to put a “1” on the bottom 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) Expand and evaluate each problem below

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13. Copyright © Lynda Greene Aguirre 2009 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 Read as: Three to the zero’th power 12

14. However, this is not equal to zero, it is defined as: 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 13

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16. Copyright © Lynda Greene Aguirre 2009 First write the base as a fraction (if it’s not already written that way) 15 Negative Exponents 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. Move the 4’s to the bottom and tear up the parking ticket (i.e. change the negative power into a positive power) Finish the problem

17. Practice Problems Copyright © Lynda Greene Aguirre 2009 16