Copyright © Lynda Greene Aguirre 2009 1 Exponential Form is used when you want to multiply the same...

Copyright © Lynda Greene Aguirre 2009 1

Copyright © Lynda Greene Aguirre 2009

Exponential FormExponential Form is used when you want to is used when you want to multiply the same number by itself several times. multiply the same number by itself several times.

455 is the base4 is the power (also called the exponent)

The The “base”“base” is is the actual the actual

numbernumber we will we will multiplymultiply

The The “power”“power” is is how manyhow many bases bases

will be will be multiplied.multiplied.

Read as: Five to the Fourth power

2


Definitions:

5 x 5 x 5 x 5 is called EXPANDED NOTATION

is called EXPONENTIAL NOTATION

45

3


For example:

five to the fourth power

45

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

Using a Calculator to evaluate exponents

Calculators use different buttons, but the most common oneis this one ^ .


Means 4 x 4 x 4 = 64

Enter it in the calculator as: 4 ^ 3 = 64

34A problem like (four to the third power)

5

Using your calculator, evaluate the following exponents:


21

211210

26

2322

2827

24

25

29

214213 215

212

6

7

Exponent ExpansionWrite in Expanded Form, then evaluate (if possible)

8Rule:

Exponent Rules

9

Exponent Rules: double powers

Rule:

Notice that you can get the same answer by multiplying the powers

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



The Exponent, or power, indicates how many bases The Exponent, or power, indicates how many bases should be multiplied. When the power is a zero, that should be multiplied. When the power is a zero, that means that there are no bases. means that there are no bases.

03The The “power”“power” indicates that indicates that

there will be no there will be no 3’s3’s

Read as: Three to the zero’th power

12

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

130 Definition of a Zero Exponent:

Anything raised to the zero’th power is equal to “1”

1)63(

1)5(

1

0

0

0

yx

x

xIt doesn’t matter what is being raised the power of zero, it will be equal to the number “1”.




First write the base as a fraction (if it’s not already written that way)

15

Negative ExponentsParking 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

2

3

2

25x

36

037x

024 x

218 x

Practice Problems

2

05

4

21

3

2

4

y

x


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Copyright © Lynda Greene Aguirre 2009 1 Exponential Form is used when you want to multiply the same...

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