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Math Help

h3nduh3ndu Registered User regular
edited May 2010 in Help / Advice Forum
Ok - so, I have a final tomorrow in math 108, intermediate algebra - I have an A in the class, and I just took the practice final online - I did well, but there was one problem that stuck me - I searched through all my notes and I couldn't find anything on it - help me please?

the problem - (125/8) [so, one hundred and twenty five over eight] to the -2/8 th power. The answer to the problem is 4/25 [four over twenty five].

If anyone could walk me through this I would be very appreciative.

Lo Que Sea, Cuando Sea, Donde Sea.
h3ndu on

Posts

  • PowerpuppiesPowerpuppies drinking coffee in the mountain cabinRegistered User regular
    edited May 2010
    first, 2/8 is 1/4, so take (125/8)^(-1/4). Negative exponents just mean take the reciprocal, so we have 1/(125/8)^(1/4). Now ( (X^m)^n) = X^(m*n), so X^(1/4)^4=X, so X^1/4 is the fourth root of X. Thus we have the reciprocal of the fourth root of 125 over 8, which is equal to the reciprocal of the fourth root of 125 divided by the fourth root of 8. This is where I start to get confused, because why would you be taking the fourth root of 5^3/2^3? Seems like it should be the third root... if I continue I get 1 / ( sqrt(5*sqrt(5)) / sqrt(2*sqrt(2)) ) which is decidedly not equal to 4/25. Did you perhaps mean to the -2/3 power?

    If so, X^(2/3) is best computed as X^(1/3)^2, so take the cuberoot and square it. So 125/8 to the -2/3 would be 8^(2/3) / 125^(2/3) = 2^2/5^2 = 4/25.

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  • enlightenedbumenlightenedbum Registered User regular
    edited May 2010
    Sure that was the question? Because pretty sure that's wrong.

    Anyway, for how to do that kind of thing:

    1) What do you do with negative exponents?
    2) What do you do with fractions raised to a power?

    enlightenedbum on
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  • h3nduh3ndu Registered User regular
    edited May 2010
    Powerpuppies wrote: »
    first, 2/8 is 1/4, so take (125/8)^(-1/4). Negative exponents just mean take the reciprocal, so we have 1/(125/8)^(1/4). X^(1/4)^4=X, so X^1/4 is the fourth root of X. Thus we have the reciprocal of the fourth root of 125 over 8, which is equal to the reciprocal of the fourth root of 125 divided by the fourth root of 8. This is where I start to get confused, because why would you be taking the fourth root of 5^3/2^3? Seems like it should be the third root... if I continue I get 1 / ( sqrt(5*sqrt(5)) / sqrt(2*sqrt(2)) ) which is decidedly not equal to 4/25. Did you perhaps mean to the -2/3 power?

    no - no, it was definetly (125/8) to the -2/8.

    I just ... seeing it in line form kind of sucks.

    ''''''''''-2/8
    125
    8

    that's the problem - and when I finished the web test it told me the answer was

    4
    ---
    25

    h3ndu on
    Lo Que Sea, Cuando Sea, Donde Sea.
  • PowerpuppiesPowerpuppies drinking coffee in the mountain cabinRegistered User regular
    edited May 2010
    h3ndu wrote: »
    Powerpuppies wrote: »
    first, 2/8 is 1/4, so take (125/8)^(-1/4). Negative exponents just mean take the reciprocal, so we have 1/(125/8)^(1/4). X^(1/4)^4=X, so X^1/4 is the fourth root of X. Thus we have the reciprocal of the fourth root of 125 over 8, which is equal to the reciprocal of the fourth root of 125 divided by the fourth root of 8. This is where I start to get confused, because why would you be taking the fourth root of 5^3/2^3? Seems like it should be the third root... if I continue I get 1 / ( sqrt(5*sqrt(5)) / sqrt(2*sqrt(2)) ) which is decidedly not equal to 4/25. Did you perhaps mean to the -2/3 power?

    no - no, it was definetly (125/8) to the -2/8.

    I just ... seeing it in line form kind of sucks.

    ''''''''''-2/8
    125
    8

    that's the problem - and when I finished the web test it told me the answer was

    4
    ---
    25

    I mean I dunno what to tell you man. The test is wrong. 125/8^(-2/3) is 4/25. 125/8^(-2/8) is not, plus what kind of math problem starts with easily reducible fractional exponents? Some sort of typo or something.

    Powerpuppies on
    sig.gif
  • h3nduh3ndu Registered User regular
    edited May 2010
    Powerpuppies wrote: »
    h3ndu wrote: »
    Powerpuppies wrote: »
    first, 2/8 is 1/4, so take (125/8)^(-1/4). Negative exponents just mean take the reciprocal, so we have 1/(125/8)^(1/4). X^(1/4)^4=X, so X^1/4 is the fourth root of X. Thus we have the reciprocal of the fourth root of 125 over 8, which is equal to the reciprocal of the fourth root of 125 divided by the fourth root of 8. This is where I start to get confused, because why would you be taking the fourth root of 5^3/2^3? Seems like it should be the third root... if I continue I get 1 / ( sqrt(5*sqrt(5)) / sqrt(2*sqrt(2)) ) which is decidedly not equal to 4/25. Did you perhaps mean to the -2/3 power?

    no - no, it was definetly (125/8) to the -2/8.

    I just ... seeing it in line form kind of sucks.

    ''''''''''-2/8
    125
    8

    that's the problem - and when I finished the web test it told me the answer was

    4
    ---
    25

    I mean I dunno what to tell you man. The test is wrong. 125/8^(-2/3) is 4/25. 125/8^(-2/8) is not, plus what kind of math problem starts with easily reducible fractional exponents? Some sort of typo or something.

    I must have misread it and then tried to solve. I can't imagine the test itself would be wrong. It has to be an error on my part. It is kind of late right now.

    Thanks for your help.

    h3ndu on
    Lo Que Sea, Cuando Sea, Donde Sea.
  • SkyCaptainSkyCaptain IndianaRegistered User regular
    edited May 2010
    Three and eights would look similar, so -2/3 could have looked like -2/8 to you.

    SkyCaptain on
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