24. Which sequence of algebraic expressions describes the following pattern?
\[
4,16,64,256
\]
A. $x, x^{2}, x^{3} ; x^{4}$
B. $x, x+12, x+24, x+48$
C. $\dot{x}, 4 x, 6 x, 8 x$
D. $\dot{x}, 2 x, 3 x, 4 x$

Step 1 ：The given sequence is a geometric sequence where each term is 4 times the previous term. This suggests that the sequence is of the form \(x, x^{2}, x^{3}, x^{4}\) where \(x=4\).

Step 2 ：Let's verify this by substituting \(x=4\) in the expression and check if we get the given sequence.

Step 3 ：Substituting \(x=4\) in the expression, we get the sequence \([4, 16, 64, 256]\).

Step 4 ：The sequence generated by substituting \(x=4\) in the expression matches the given sequence.

Step 5 ：Therefore, the algebraic expression that describes the given sequence is \(x, x^{2}, x^{3}, x^{4}\) where \(x=4\).

Step 6 ：Final Answer: \(\boxed{\text{A. } x, x^{2}, x^{3}, x^{4}}\)