Final answer:
The next number in the given pattern (1, 4, 16, 64) is found by continuing the multiplication by 4, resulting in the next number being 256.
Step-by-step explanation:
The student is asking for the next number in the sequence 1, 4, 16, 64. To find the pattern, we observe that each number is the product of the previous number and a constant multiplier. Specifically, each number is 4 times the previous number in the sequence (4 × 1 = 4, 4 × 4 = 16, 4 × 16 = 64). Thus, to find the next number, we multiply the last number in the sequence by 4.
64 × 4 = 256
Therefore, the next number in the pattern is 256.