Write a formula for the $\mathrm{nth}$ term of the following geometric sequence. Then use the formula for $a_{n}$ to find $a_{6}$, the 6 th term of the sequence.
$4,16,64, \ldots$
Enter a formula for the $\mathrm{nth}$ term of the geometric sequence.
\[
a_{n}=\square \cdot(\square)^{n-1}
\]

Step 1 ：The given sequence is a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio is 4 (16/4 = 4, 64/16 = 4).

Step 2 ：The formula for the nth term of a geometric sequence is given by: \(a_{n} = a_{1} \cdot r^{(n-1)}\) where: \(a_{n}\) is the nth term of the sequence, \(a_{1}\) is the first term of the sequence, r is the common ratio, n is the term number.

Step 3 ：In this case, \(a_{1}\) = 4 and r = 4. So, the formula for the nth term of the sequence is: \(a_{n} = 4 \cdot 4^{(n-1)}\)

Step 4 ：Now, we can use this formula to find the 6th term of the sequence. \(a_{1}\) = 4, r = 4, n = 6, \(a_{n}\) = 4096

Step 5 ：Final Answer: The 6th term of the sequence is \(\boxed{4096}\)