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How does one side equal the other

  1. Apr 10, 2013 #1
    1. The problem statement, all variables and given/known data

    I know this isnt exactly calculus related but it is from working out a calculus problem

    I was wondering how:
    (8/27) * [103/2 - (13/4)3/2]

    equals

    (1/27) * [80 * sqrt(10) - 13 * sqrt(13)]



    3. The attempt at a solution

    All i can conclude from this answer is that they multiplied 8 throughout the equation but i don't understand the rest of it, it doesn't make sense
     
  2. jcsd
  3. Apr 10, 2013 #2

    Mark44

    Staff: Mentor

    They didn't multiply 8 "throughout the equation." This is an expression, and they are using the distributive property like this: a(b + c) = ab + ac.

    (8/27) * [103/2 - (13/4)3/2]
    = 1/27 * [8 * 10 √10 - 8 * (13/4) * √(13/4)]
    Can you continue from here?
     
  4. Apr 10, 2013 #3
    ##\frac{8}{27} [10^{3/2} - (\frac{13}{4}) ^{3/2}] = (1/27) [80 \sqrt{10} - 13 \sqrt{13}]##

    Remember that ##x^{a/b} = \sqrt{x} ^a## and ##(\frac{a}{b}) ^y = \frac{(a^y)}{(b^y)}##
    Now try distributing the 8 and using those rules.
     
  5. Apr 10, 2013 #4
    i understand that part but where did the power of 3 go?
     
  6. Apr 10, 2013 #5

    Mark44

    Staff: Mentor

    103/2 = 101 + 1/2 = 10 * √10
     
  7. Apr 10, 2013 #6
    wow am i really that dumb?

    this whole time i was thinking

    103/2 was equal to (√10)3

    man, its been a rough day for me, thanks mark.
     
  8. Apr 10, 2013 #7
    By the way, it does.

    10^(3/2) = (√10)^3 = (√10)*(√10)*(√10) = (√10)*(√10)^2 = (√10)*10
     
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