college algebra

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factor...
(x+4)^-3/5+(x+4)^-1/5+(x+4)^1/5

Please explain the process used to solve this type of expression. Answer should be in equation form if that helps....

  • college algebra -

    consider a simpler case:
    x^5 + 2x^3 + 5x^2

    the common factor is x^2, that is, the power with the smallest exponent, so

    x^2(x^3 + 2x + 5)
    how did we get the terms inside ?
    We subtracted the exponent of the common factor from the original exponent.

    now to our question,
    (x+4)^-3/5+(x+4)^-1/5+(x+4)^1/5
    clearly the base of (x+4) becomes part of the common factor,
    what is the smallest exponent ? it is -3/5
    so (x+4)^(-3/5) is the common factor

    answer:
    (x+4)^(-3/5)[1 + (x+4)^(2/5) + (x+4)^(4/5)]

    you can check this answer by expanding it, remember when multiplying powers we add the exponents

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