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Math Help - Simplify Expression for y

  1. #1
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    Simplify Expression for y

    Simplify for y.

    I have to simplify what y equals to.

    y = 1 divided by n(x^[(1/n)(n - 1)]

    Everything in red is the exponent of x.

    How do I simplify what y equals to?

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  2. #2
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    Quote Originally Posted by sharkman View Post
    Simplify for y.

    I have to simplify what y equals to.

    y = 1 divided by n(x^[(1/n)(n - 1)]

    Everything in red is the exponent of x.

    How do I simplify what y equals to?
    Multiply out the factors in the exponent of x. That will simplify the exponent. Then, remember your laws of exponents. How can you move something in the denominator up to the numerator?
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  3. #3
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    ok...but

    Quote Originally Posted by QM deFuturo View Post
    Multiply out the factors in the exponent of x. That will simplify the exponent. Then, remember your laws of exponents. How can you move something in the denominator up to the numerator?
    In the numerator, we have (1/n)(n - 1).

    (1/n)(n - 1) = (n - 1)/n...This is the new exponent.

    You also said:

    "Then, remember your laws of exponents. How can you move something in the denominator up to the numerator?"

    Can you show me the rest of the way?

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  4. #4
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    Quote Originally Posted by sharkman View Post
    In the numerator, we have (1/n)(n - 1).

    (1/n)(n - 1) = (n - 1)/n...This is the new exponent.

    You also said:

    "Then, remember your laws of exponents. How can you move something in the denominator up to the numerator?"

    Can you show me the rest of the way?

    Remember that  \frac{1}{a^b} = \frac{a^{-b}}{1}
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  5. #5
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    then...

    Quote Originally Posted by QM deFuturo View Post
    Remember that  \frac{1}{a^b} = \frac{a^{-b}}{1}
    I'll have to play with this one some more.
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  6. #6
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    Talking

    I will take the equation to be as follows:

    . . . . . y\, =\, \frac{1}{nx^{\left(\frac{1}{n}\right)(n\, -\, 1)}}

    If so, then note that (1/n)(n - 1) = -(1/n)(1 - n), and negative exponents mean to move the base to the other side of the fraction line, so we get:

    . . . . . y\, =\, \frac{x^{\left(\frac{1}{n}\right)(1\, -\, n)}}{n}

    I'm not sure that anything "simplifies" much after this point....
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  7. #7
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    Quote Originally Posted by stapel View Post

    y\, =\, \frac{x^{\left(\frac{1}{n}\right)(1\, -\, n)}}{n}

    I'm not sure that anything "simplifies" much after this point....
    Well, not much. But you could do :

     (\frac{1}{n})(1 - n) = (\frac{1}{n} - 1 )

    That's slightly simpler
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  8. #8
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    ok....

    Quote Originally Posted by QM deFuturo View Post
    Well, not much. But you could do :

     (\frac{1}{n})(1 - n) = (\frac{1}{n} - 1 )

    That's slightly simpler
    Yes, that is as simple as it gets.
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