Posted by **coried** on Friday, July 24, 2009 at 9:30pm.

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 -
**Reiny**, Friday, July 24, 2009 at 11:10pm
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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