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Powers with rational exponents: write as single power then evaluate. (Review My Work)

  1. Mar 21, 2012 #1
    1. The problem statement, all variables and given/known data
    Write as a single power, then evaluate:
    a) (-32)^3/5 x (-32)^-4/5 / (-32)^2/5


    b) 4096^3/6 / 4096^2/3 x 4096^5/6

    2. Relevant equations



    3. The attempt at a solution

    a) (-32)^3/5 x (-32)^-4/5 / (-32)^2/5
    = (-32)^3/5+(-4/5)-2/5
    = -32^-3/5
    = -1/8 <- not sure about this

    b) 4096^3/6 / 4096^2/3 x 4096^5/6
    = 4096^(9-8+10)/12
    = 4096^11/12

    I'm not so sure of where to go from here.
     
  2. jcsd
  3. Mar 21, 2012 #2
    Re: Powers with rational exponents: write as single power then evaluate. (Review My W

    Your first answer is right :-)

    Second needs some review.

    Remember (x^a*x^b)/(x^c*x^d)

    Is x^(a+b-c-d)

    So its 4096^(3/6-2/3-5/6)


    You have made a mistake by writing 4096^({9}-8-10)/12

    It shouldn't be 9 in the curly brackets i put{} :-).

    Also factorise 4096.
    Write it in power of primes.

    For eg 400=2^4*5^2

    So (400)^(1/2)

    Is
    [(2^4)*(5^2)]^(1/2)

    So its (2^2)*(5) which gives 20.
     
    Last edited: Mar 21, 2012
  4. Mar 21, 2012 #3
    Re: Powers with rational exponents: write as single power then evaluate. (Review My W

    Oh man I copied down the wrong problem. I'm so sorry. It was supposed to be:
    4096^3/4 / 4096^2/3 x 4096^5/6
    I got the common denominator which would been 12. That is how I got 4096^(9-8+10)/12
    = 4096^11/12

    am I still incorrect?
     
  5. Mar 21, 2012 #4

    Dick

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    Re: Powers with rational exponents: write as single power then evaluate. (Review My W

    You should probably use parentheses instead of spaces to make that clearer. If you mean (4096^(3/4)/4096^(2/3))*4096^(5/6) then 4096^(11/12) is correct. There's a much simpler way to express that answer. 4096^(1/12)=2.
     
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