To find the possible values of "b" in the equation a^(b/4) = 16, we need to consider the properties of exponents and solve the equation step by step.


We can rewrite the equation as a^(b/4) = 2^4, since 16 is equal to 2^4.


Using the property of exponents which states that a^(b/c) = (a^b)^(1/c), we can rewrite the equation as (a^b)^(1/4) = 2^4.


Now, we have (a^b)^(1/4) = 2^4. By raising both sides of the equation to the power of 4, we can simplify it further.

((a^b)^(1/4))^4 = (2^4)^4
(a^b)^1 = 2^(4*4)
a^b = 2^16


Now, we need to find the possible values of "b" that satisfy the equation a^b = 2^16.

Since a and b are positive integers, we can see that 2^16 is a large number (65536). Therefore, we need to find a value of "b" that results in a^b being equal to 65536.

We can start by trying different values of "b" and calculating a^b until we find a value that equals 65536.

Let's try a few values of "b":

- b = 2: a^2 = 65536 (not equal to 65536)
- b = 3: a^3 = 65536 (not equal to 65536)
- b = 4: a^4 = 65536 (not equal to 65536)
- b = 5: a^5 = 65536 (not equal to 65536)
- b = 6: a^6 = 65536 (not equal to 65536)

After trying several values of "b", we can see that there is no positive integer value of "b" that satisfies the equation a^b = 2^16. Therefore, there is no possible value for "b" that satisfies the given equation.

Therefore, the value of "b" is not possible to determine in this scenario.