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  1.  
  2.                        Review of Exponents and Radicals
  3.                        ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀
  4.  
  5.  
  6. If a and b are positive integers:
  7.  
  8.  
  9.                                 a b      a+b
  10.                                x x   =  x 
  11.  
  12.  
  13.                              a
  14.                             x        a-b       1
  15.                            ────  =  x    =  ──────
  16.                              b                b-a
  17.                             x                x
  18.  
  19.  
  20.                                a  b      ab
  21.                              (x )    =  x
  22.  
  23.  
  24.                                   a      a a
  25.                               (xy)   =  x y
  26.  
  27.  
  28.                                   a      a    a
  29.                              (x/y)   =  x  / y
  30.  
  31.  
  32.                                 O
  33.                                x     =  1    ( if x ╪ O )
  34.  
  35.  
  36.                                 -a           a
  37.                                x     =  1 / x
  38.  
  39.                                           _____
  40.                                 a/b     b ▌  a
  41.                                x     =   \▌ x
  42.  
  43.  
  44.                                 -a/b         a/b
  45.                                x     =  1 / x
  46.  
  47.                              _____
  48.                            b ▌            1/b
  49.                             \▌ x     =   x
  50.  
  51.  
  52.                      _____    _____       _____
  53.                    b ▌      b ▌         b ▌
  54.                     \▌ x     \▌ y    =   \▌ xy  
  55.  
  56.  
  57.                              ____
  58.                            b ▌            ____
  59.                             \▌ x        b ▌ x
  60.                            ───────   =    ▌───
  61.                              ____        \▌ y
  62.                            b ▌   
  63.                             \▌ y
  64.  
  65.  
  66.  
  67. ┌─────────────────┐
  68. │ Common Mistakes │
  69. └─────────────────┘
  70.                                        _______         __    __
  71. NOTE:  There is NO formula relating   \▌x + y    to   \▌x + \▌y . 
  72. This is the biggest single mistake we see in this area.  If you make this
  73. mistake it is very unlikely you'll ever do well in calculus.
  74.  
  75.  
  76.                -1/3      1                      -1/3        1
  77. WRONG         x      =  ────         RIGHT     x       =  ─────
  78.                           3                                 1/3
  79.                          x                                 x
  80.  
  81.            _________                          ________
  82.            ▌  2                               ▌  2
  83. WRONG     \▌ x  + 1    =  x + 1      RIGHT   \▌ x  + 1  cannot be simplified.
  84.  
  85.  
  86.           _________     _________              _________      __________
  87.           ▌      2      ▌  2    3              ▌      2       ▌  3    4
  88. WRONG   x\▌ x + x   =  \▌ x  + x     RIGHT   x\▌ x + x    =  \▌ x  + x
  89.  
  90.  
  91.  
  92.  
  93. This is the end of the help file.  Press the ESC key to return to the quiz
  94. question you were doing.
  95.