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How do I factorize this expression? $$(2^n-3^n+n4^n)^{\frac{1}{n}}$$ so far I have: $$n4^n\left(\frac{1}{n} \left(\frac{1}{2}\right)^n-\frac{1}{n}\left(\frac{3}{4}\right)^n +1\right)^{\frac{1}{n}}$$

Forgot to mention the limits part of this question. How would I calculate the limit for this?

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You have the word "limits" in the title, you should mention them in your question. – anon Mar 17 '13 at 23:14
Where does factorization come into this problem? What limit are you trying to compute? – Gerry Myerson Mar 17 '13 at 23:17
up vote 3 down vote accepted

I don't see how this can be factored.

For the limit, if you take the $4^n$ out of the parens, the expression becomes $4(n-(3/4)^n+(1/2)^n)^{1/n}$ and this goes to 4 since $n^{1/n} \to 1$.

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