exponents

Exponents

VINCENT LEPING

08/03/2014

For Learning to Happen!

•Clear your desk of anything that may distract you.

•Remove all other thoughts from your mind.

•Pay close attention.•Try all the examples.•Ignore all other distractions.

Definition of Exponent

An exponent tells how many times a number is multiplied by itself.

3 4Base

Exponent

Review:

What do exponents tell us?

What does 53 mean?

53 =5 5 5

What is the “base”?What is the “exponent”?

8 5BaseExponent

What an Exponent Represents

An exponent tells how many times a number is multiplied by itself.

34= 3 x 3 x 3 x 3

Write 63 in standard form.

63 = 6 6 6 = 216

Write 64 in standard form.64 = 6 6 6 6

= 1,296

What happens if we multiply 63 64?63 64=(6 6 6) (6 6 6 6)

63 64

So…63 64= 67 because we used 6 as a factor seven times!

Notice anything?

Let’s try another example:

What is 52 54?

52 54 = (5 5) (5 5 5 5)

or 52 54 = 56

For MULTIPLICATION:

x s x t = x s + t

(For any number x and for integers s and t.)

In other words, when multiplying two numbers in exponential form with the same base, add the exponents.

Ex:9 4 9 8 = ?

9 12

What happens if we divide?75

73

75 = 7 7 7 7 7

73 7 7 7

Cancel out any numbers that are in the numerator AND denominator!

After we cancel, we are left with 72.

So, 75 = 72

73

For DIVISION:

xs =

xt

(For any nonzero number x and for integers s and t.)

x s - t

In other words, when dividing two numbers in exponential form with the same base, subtract the exponents.

Ex:6 8 ÷ 6 5 = ?

6 3

What about (52)3?(52)3

(52) (52) (52)

(5 5)(5 5)(5 5)

56

Raising a power to a power:

(xs)t = x s t

(For any number x and for integers s and t.)

In other words, when raising a number with an exponent to a power, multiply the exponents.

Ex:(5 3) 7 = ?

521

One important thing to remember…x0 = 1

(Any number to the zero power is equal to 1!)

Why???For example…

32 ÷ 32 = 3 2 - 2 = 30

32 = 3 3 = 9 = 1

32 3 3 9

So, 30 = 1This works for any base number!

Can we have negative exponents?

Yes! Negative exponents represent the reciprocal.

The reciprocal of x is

The reciprocal of 10 is

They do NOT make the answer negative.

x

1

10

1

5 -2 = =

2-4=

25

1

25

1

16

1

2

14

REFERENCE LIST

Melnichenko, Y. (2008, September 14). Exponents. Retrieved March 08, 2014, from http://www.slideshare.net/yelena585/exponents-presentation

Yuskaitis, M. (2008, June 06). Exponents. Retrieved March 08, 2014, from http://www.slideshare.net/hiratufail/exponents1