What is the square root of 16 raised to the fourth power?

To solve the problem, you need to follow the order of operations and understand the properties of exponents and square roots.

First, calculate the square root of 16. The square root of 16 is 4 because 4 multiplied by 4 equals 16.

Next, you then raise this result (4) to the fourth power. When you raise a number to a power, you multiply the number by itself the number of times indicated by the exponent. Therefore, 4 raised to the fourth power is calculated as follows:

[ 4^4 = 4 \times 4 \times 4 \times 4 ]

Calculating it step by step:

1. ( 4 \times 4 = 16 )

2. ( 16 \times 4 = 64 )

3. ( 64 \times 4 = 256 )

Thus, ( 4^4 = 256 ).

This is why the answer is 256. Understanding how to apply the properties of exponents and performing calculations in the correct order leads to the answer.