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