Identify the function represented by the following power series.
\[
\sum_{k=0}^{\infty}(-1)^{k} \frac{x^{4 k}}{6^{k}}
\]
\# Click the icon to view a table of Taylor series for common functions.
\[
f(x)=
\]

Step 1 ：Identify the function represented by the following power series: \[\sum_{k=0}^{\infty}(-1)^{k} \frac{x^{4 k}}{6^{k}}\]

Step 2 ：The given power series is a geometric series with common ratio of \(-\frac{x^4}{6}\).

Step 3 ：The sum of a geometric series is given by the formula \(\frac{a}{1-r}\), where \(a\) is the first term and \(r\) is the common ratio.

Step 4 ：In this case, the first term \(a\) is 1 (when \(k=0\)), and the common ratio \(r\) is \(-\frac{x^4}{6}\).

Step 5 ：So, the function represented by the power series is \(f(x) = \frac{1}{1+\frac{x^4}{6}}\).

Step 6 ：Simplify the function to get the final answer: \(f(x) = \frac{6}{x^{4} + 6}\).

Step 7 ：\(\boxed{f(x) = \frac{6}{x^{4} + 6}}\) is the function represented by the power series.