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Exponents

Page history last edited by PBworks 16 years, 5 months ago
( are awesome )
 
 
 Exponents are the representation of a number in the form:
           Xy
 
(X is the base and y is the exponent.)
The exponent is the number of times the base is multipied by itself. 
X to the y power.
 
 
 
Example:
53
(5 is the base and 3 is the exponent.)
53 = 5 x 5 x 5 = 125
This process of using exponents is called "raising to a power", where the exponent is the "power". "53" is "five,
 
raised to the third power". When we use numbers, we usually just simplify; we'd rather deal with "27" than
with "33".  But with variables, we need the exponents, because we'd rather deal with "x6" than with "xxxxxx".
                    27 =  33                                                                    x6 = xxxxxx
 
 
There are some special cases:
  • A number to the 1st power is itself.
         a1 = a
                 61 = 6
  • When an exponent is zero, than the answer is always equal to 1.

            a0 = 1

                   60 = 1

 

 

                            

                1. am * an = a(m+n)

             2. (a * b)n = an * bn

          3. (am)n = a(m * n)

          4. am / an = a(m-n)

          5. (a/b)n = an / bn

 

 

 

 

Reciprical Property

A number in exponential notation can also be expressed in terms of its recipricol. The reciprocal of a number raised to the exponent a is that number raised to the exponent -a .

Therefore,

 

 

 

                                                    X a = 1 / X-a

 

X -a = 1 / Xa

 

                               2-3 = 1 / 23 = 1 / 8

 

 

 

 

 

Multiplication Property 

When two exponential numbers having same base are multipled, their exponents are added.

If k and t are numbers, then

 

 

Xk * Xt = Xk+t

 

                     243 * 81 = 35 * 34 = 35+4 = 39 = 19,683

 

 

 

 

 

 

 

 

 

It is important to make sure that the two exponential numbers that are multiplied should have the same base!!

 

 

                16 * 1024 = 24 * 45 = 24 * (22)5 = 24X 210 = 214 = 16,384

 

 

 

In the table below, the number 2 is written as a factor repeatedly. The product of factors is also displayed in this table. Suppose that Mr. Martin asked you to write 2 as a factor one million times for homework.  :(  How long do you think that would take?  That's why we have EXPONENTS!!!

 

                   

Factors Product of Factors Description
2 x 2 = 4 2 is a factor 2 times
2 x 2 x 2 = 8 2 is a factor 3 times
2 x 2 x 2 x 2 = 16 2 is a factor 4 times
2 x 2 x 2 x 2 x 2 = 32 2 is a factor 5 times
2 x 2 x 2 x 2 x 2 x 2 = 64 2 is a factor 6 times
2 x 2 x 2 x 2 x 2 x 2 x 2 = 128 2 is a factor 7 times
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 2 is a factor 8 times
                                        

  

 

 

 

 

 http://www.mclph.umn.edu/mathrefresh/exponents.html

 http://www.mclph.umn.edu/mathrefresh/exponents2.html

 http://cs.gmu.edu/cne/modules/dau/algebra/exponents/exp1_frm.html

 http://www.purplemath.com/modules/exponent.htm

 http://www.math.com/school/subject2/lessons/S2U2L2GL.html

 http://www.mathgoodies.com/lessons/vol3/exponents.html

 

 

 

Comments (22)

Anonymous said

at 7:03 pm on Oct 24, 2007

I like your title! :]

Anonymous said

at 8:52 pm on Oct 24, 2007

OMG Stephanie I Love ur examples and ur title!
bye.laurie.

Anonymous said

at 10:50 pm on Oct 28, 2007

You spelled reciprocal wrong in reciprocal property.

Anonymous said

at 12:22 pm on Oct 29, 2007

nice font for title

Anonymous said

at 1:35 pm on Oct 29, 2007

how`d yu do ur title like that?

Anonymous said

at 4:48 pm on Nov 1, 2007

NICE PAGE! :)

Anonymous said

at 9:49 am on Nov 5, 2007

STEPHANIE FONG!!!
i hate chu cuz ur page is so prettiful....
i think that ur page is very helpful if sumone need help on exponents butyu should try putting somethings in ur own word...

Anonymous said

at 9:54 am on Nov 5, 2007

nice page, but the words are really small at the end.

Anonymous said

at 9:59 am on Nov 5, 2007

STEFF!! i love it but make your font bigger

Anonymous said

at 1:05 pm on Nov 5, 2007

ITs awesome

Anonymous said

at 1:09 pm on Nov 5, 2007

your page is good and i like your examples and your info is very helpful.

Anonymous said

at 1:11 pm on Nov 5, 2007

nice work!!! cool font!!!

Anonymous said

at 1:13 pm on Nov 5, 2007

You have good infromation.

Anonymous said

at 1:17 pm on Nov 5, 2007

your info is good

Anonymous said

at 1:24 pm on Nov 5, 2007

DUUUUUUUUUDEEEEE-ette haha lol your page has lotsa info on it!!! its like woooooooowwwwww its REALLY nice and all hhahah yeahh colorful, pretty, awesome, lol its SUPER DEE DUPER!! haha lol

Anonymous said

at 2:33 pm on Nov 5, 2007

this is really nice
but maybe some more links?

Anonymous said

at 9:29 pm on Nov 7, 2007

omg steff. that's soo good. how'd you get that backround?? really cool.

Anonymous said

at 10:49 pm on Nov 7, 2007

whoaaaah how'd you do that? how'd you make the background &the title like hecka cool writing? let me know @school or something, kthanks.[= NICE PAGE THOE.

Anonymous said

at 11:04 pm on Nov 10, 2007

okay you have to tell me how you got that backround. pleassee!!!

Anonymous said

at 10:07 am on Nov 12, 2007

thanks stephanieee.

Anonymous said

at 1:33 pm on Nov 13, 2007

OMG. I really love the backround and all of the cool fonts <3

Anonymous said

at 12:03 am on Nov 22, 2007

Very good. Did you send me an email about comments?

4 of 4 points
10 of 12 total project points

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