Question Breakdown:
The question asks to find the value of 16 raised to the power of the logarithm of 4 raised to the power of 5. In other words, we need to calculate 16^(log(4^5)).

Solution:
To find the value of 16^(log(4^5)), we can break it down step by step.

Step 1: Calculate the value of 4^5
To find 4^5, we simply multiply 4 by itself 5 times:
4^5 = 4 × 4 × 4 × 4 × 4 = 1024

Step 2: Calculate the logarithm of 1024
The logarithm of a number tells us what exponent we need to raise a base to in order to get that number. In this case, we need to find log(1024).

Step 3: Calculate the value of 16 raised to the power of log(1024)
Now that we have the value of log(1024), we can substitute it into the original expression:
16^(log(1024))

Step 4: Simplify the expression
To simplify the expression, we can rewrite 16 as 2^4 since 16 is equal to 2 raised to the power of 4:
(2^4)^(log(1024))

Step 5: Apply the exponent rule
According to the exponent rule, when we raise a power to another power, we multiply the exponents:
2^(4 × log(1024))

Step 6: Simplify the expression further
Now we can simplify the expression by multiplying 4 by log(1024):
2^(4 × log(1024))

Step 7: Calculate the value of log(1024)
Since log(1024) = 5, we can substitute it into the expression:
2^(4 × 5)

Step 8: Calculate the final value
Now we can simplify the expression further:
2^20 = 1048576

Final Answer:
The value of 16^(log(4^5)) is 1048576.