Exponents

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					Exponent Rules:

XY = X multiplied by itself Y times.   For example: 24 = 2222 = 16

Given that, here are some useful rules that you can use to make the process of dealing
with exponents much more pleasant:

 Rule:                Example:

 A-k = 1/Ak           2-3 = 1/(222) = 1/8

 AkAn = A(k+n)       3233 = (33)  (333) = 33333 = 35

 Ak/An = A(k-n)       32/33 = (33) / (333) = 1/3 = 3-1

                      (32)3 = (33)  (33)  (33) = 333333
 (Ak)n = A(kn)       = 36

        So use the rules above to convert the complicated exponent forms into a simple
exponent form. Check your answers against those at the end of this sheet to catch and
correct any mistakes you might have made…

   52  54        =
   67  63        =
 101  10-        =
       3

  8-9  85        =
  38 / 34         =
  22 / 25         =
   107 /
                  =
    1012
   10-3 /
                  =
    10-8
    (44)5         =
    (97)4         =
    (72)-3        =
                                              Answers: 56,610,10-2,8-4,34,2-3,10-5,105,420,928,7-6

      Digging for Roots:
              If you want to have your calculator take the square root of something it’s pretty
      straightforward once you’ve found the        button. Taking higher roots of a number,
      however, often require that you know the rule illustrated below.

      a  X  X 1 2  X 0.5       (where a is the square root ofX)
                                      
      b  3 Y  Y 1 3  Y 0.333   (where b is the cube root ofY )

      c  4 Z  Z1 4  Z 0.25     (where c is the fourth root ofZ)

      The critical fact is that the “nth root” of a number is the same as that number raised to the
      1/n power. So if you wanted to know what the cube root of 125 was you could plug the
    following into your calculator:

      125^(1/3)    [enter]                                           125^(0.3333) [enter]
                                                   OR
               = 5                                                            = 5


             Now, to practice, use your calculator to determine the answers to the following
      problems and then check your answers against the answers below to catch and correct
      any mistakes you might have made…


       5
              1024 
          3
              216    
          4
              625    
          2
              100    
          4
              500 
          5
              243 
      2
           1000 
          3
              900 




Answers: 4, 6, 5, 10, 4.7287, 3, 31.623, 9.6549

				
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