
                       Review of Exponents and Radicals
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If a and b are positive integers:


                                a b      a+b
                               x x   =  x 


                             a
                            x        a-b       1
                           ────  =  x    =  ──────
                             b                b-a
                            x                x


                               a  b      ab
                             (x )    =  x


                                  a      a a
                              (xy)   =  x y


                                  a      a    a
                             (x/y)   =  x  / y


                                O
                               x     =  1    ( if x ╪ O )


                                -a           a
                               x     =  1 / x

                                          _____
                                a/b     b ▌  a
                               x     =   \▌ x


                                -a/b         a/b
                               x     =  1 / x

                             _____
                           b ▌            1/b
                            \▌ x     =   x


                     _____    _____       _____
                   b ▌      b ▌         b ▌
                    \▌ x     \▌ y    =   \▌ xy  


                             ____
                           b ▌            ____
                            \▌ x        b ▌ x
                           ───────   =    ▌───
                             ____        \▌ y
                           b ▌   
                            \▌ y



┌─────────────────┐
│ Common Mistakes │
└─────────────────┘
                                       _______         __    __
NOTE:  There is NO formula relating   \▌x + y    to   \▌x + \▌y . 
This is the biggest single mistake we see in this area.  If you make this
mistake it is very unlikely you'll ever do well in calculus.


               -1/3      1                      -1/3        1
WRONG         x      =  ────         RIGHT     x       =  ─────
                          3                                 1/3
                         x                                 x

           _________                          ________
           ▌  2                               ▌  2
WRONG     \▌ x  + 1    =  x + 1      RIGHT   \▌ x  + 1  cannot be simplified.


          _________     _________              _________      __________
          ▌      2      ▌  2    3              ▌      2       ▌  3    4
WRONG   x\▌ x + x   =  \▌ x  + x     RIGHT   x\▌ x + x    =  \▌ x  + x




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