#### Answer

Converges

#### Work Step by Step

Consider $a_n=\dfrac{n^4}{(-4)^n}$
and $|a_n|=|\dfrac{n^4}{(-4)^n}|=\dfrac{n^4}{4^n}$
Now, $l=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n}} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{(n+1)^4}{4^{n+1}}}{\dfrac{n^4}{4^n}}|$
Thus, we have $l=\lim\limits_{n \to \infty}|\dfrac{(n+1)^4}{4n^4}|=\dfrac{1}{4} \lt 1$
Hence, the series Converges absolutely by the ratio test.