To find the 9th term of the geometric sequence given, we first need to identify the first term and the common ratio.
The first term \( a_1 \) is 4.
Next, we need to find the common ratio \( r \). This can be found by dividing the second term by the first term:
\[ r = \frac{-16}{4} = -4 \]
Now that we have the first term \( a_1 = 4 \) and the common ratio \( r = -4 \), we can use the formula for the \( n \)-th term of a geometric sequence:
\[ a_n = a_1 \cdot r^{(n-1)} \]
To find the 9th term \( a_9 \):
\[ a_9 = a_1 \cdot r^{(9-1)} = 4 \cdot (-4)^{8} \]
Now we need to calculate \( (-4)^{8} \):
\[ (-4)^{8} = (4^8) = 65536 \]
Now substitute back into the equation for \( a_9 \):
\[ a_9 = 4 \cdot 65536 = 262144 \]
Thus, the 9th term of the geometric sequence is:
\[ \boxed{262144} \]