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Algebra and Exponents... it's been 8 years

Kewop DecamKewop Decam Registered User regular
edited April 2008 in Help / Advice Forum
(64X^6)^-1/3 (2y^-1) (2xy)^2

I havne't done this kind of math since highschool and I know it's easy, but I can't figure it out for the life of me. Can someone break it down so I can figure this junk out.

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Posts

  • StaxeonStaxeon Buffalo, NYRegistered User regular
    edited April 2008
    Please excuse my dear Aunt Sally.

    Staxeon on
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  • the wookthe wook Registered User regular
    edited April 2008
    negative exponents are equivalent to one over the exponent

    x^-4 = 1/x^4
    2x^-4 = 2/x^4

    fractional exponents are equivalent to that root

    x^1/2 = sqrt(x)
    x^1/3 = third root of x

    the wook on
  • RaereRaere Registered User regular
    edited April 2008
    (64X^6)^-1/3 (2y^-1) (2xy)^2

    I havne't done this kind of math since highschool and I know it's easy, but I can't figure it out for the life of me. Can someone break it down so I can figure this junk out.

    I haven't done math in a while either, but let me try, my thought process might be similar. I'm using a calculator here for the arithmetic and exponents. This is just my attempt, it may or may not be right.

    I spoilered the answers in case you want to do it yourself. To do exponents you can just get a calculator (I used the Windows one) and find a key like x^y where x is the number and y is the exponent, like -1/3 or something.

    Break the problem into three parts.

    1.) 64X to the sixth power is
    68,719,476,736X
    Now raise that to the -1/3rd power and you get
    4,096X

    2.) 2Y to the -1 power is
    0.5Y

    3.) 2XY to second power (squared) is
    4XY

    Now to combine them...and where I get a little foggy.
    4,096X times 0.5Y
    (answer from steps 1 and 2) gives you
    2,048XY
    (I think you just take care of the numbers then add in the variables, X and Y)
    2,048XY times 4XY
    (answer from the previous part and step 3) and your final answer is
    8,192XY^2
    (I think you take care of the numbers again and add in the variables, which are now squared because there's two of X and two of Y)

    The numbers are probably right,
    8,192
    is a nice clean exponent of 2. Not sure about the variables, though. I don't know if you can stick em together like that, and if you just square them because there's two of each.

    Raere on
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  • CycloneRangerCycloneRanger Registered User regular
    edited April 2008
    All you did was post an expression in X and Y. What are you trying to do with it? Differentiate it? Integrate it? Solve it for some values of X and Y?

    You need to give us a lot more information.

    CycloneRanger on
  • the wookthe wook Registered User regular
    edited April 2008
    Raere, your order of ops are all jacked

    64x^6 equals 64(x^6), not (64x)^6
    (64x^6)^-1/3 = 1/((64x^6)^1/3) = 1/(4x^2)

    2y^-1 = 2/y

    (2xy)^2 = 4x^2y^2

    (1/(4x^2)) (2/y) (4x^2y^2)

    the 4x^2 in the denominator of the first term cancels the 4x^2 in the numerator of the third, so you get

    1 (2/y) (y^2)

    the y in the denominator of the second term is cancelled by one of the ys in the third, so you get

    1 * 2 * y = 2y

    unless i've radically missed my mark

    the wook on
  • GoodOmensGoodOmens Registered User regular
    edited April 2008
    CycloneRanger, I'm assuming he wants to simplify it, and if so, I concur with the wook. The key things to keep in mind when dealing with exponents are:
    1. Negative exponent=reciprocal
    2. Fractional exponent=radical
    3. Watch your parentheses carefully, and make sure you know exactly what is, and what isn't, being raised to any given exponent. That's where Raere ran into trouble.

    GoodOmens on
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  • ASimPersonASimPerson Cold... and hard.Registered User regular
    edited April 2008
    Yeah, unless the OP is missing a parenthesis or two, the wook has it right.

    ASimPerson on
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