Changing the Form of Expressions

Rearranging coefficients and exponents

Often changing in the coefficients or exponents of an expression will be sufficient to give it a new and more useful form. This is illustrated by the following examples.

Examples
Note for each example how we have rearranged the coefficients of the problem, and what exponents we have rewritten.
  1. (x/2) = (1/2) x
  2. 3/(4(2r+1)^(10)) = (3/4)(2r+1)^(-10)
  3. 2^(-n) = (2^(-1))^n = (1/2)^n
  4. 2^(x+3) = 2^x 2^3 = 8 2^x
  5. (3x + sqrt(2x))/sqrt(x) = (3x/sqrt(x)) + sqrt(2x)/sqrt(x) = 3x^(1 - 1/2) + sqrt(2)sqrt(x)/sqrt(x) = 3x^(1/2) + sqrt(2)
Practice

Be sure you've gone through each step in the examples above before doing these. Once you've worked them until you're sure that you understand them, go on to the next section. There are more problems of this type in the section test at the end of the section.

Note that you can get new practice problems by clicking the "Refresh" button at the bottom of the practice set.

  1. Rewrite the following expression in the form
    a b^x
    a ^b ^( ^x ^+ ^c ^)   =   ^x
    (Enter answers, then click: . Answer message: )
  2. Rewrite the following expression in the form
    a x^m + b x^n
    d x ^g + ( n x ) ^1 ^/ ^j
    .
      k   x ^m  
       
      =   x   + x  
    (Enter answers, then click: . Answer message: )
For more practice, click: .
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precal: 5.1 - rewriting expressions
page created: Sat Apr 27 07:21:13 2024
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©2003-2007 Gavin LaRose, Pat Shure / University of Michigan Math Dept. / Regents of the University of Michigan