Question

Which of the following expressions is equal to [f(r)]^s

Answer 1

f(x)=a^x
[f(r)]^s=?
x=r→f(r)=a^r
[f(r)]^s=(a^r)^s→[f(r)]^s=a^(r*s)

x=r^s→f(r^s)=a^(r^s) different to a^(r*s)=[f(r)]^s
x=r*s→f(r*s)=a^(r*s)=[f(r)]^s
x=r+s→f(r+s)=a^(r+s) different to a^(r*s)=[f(r)]^s

Answer: Second option f(r*s)

Answer 2

If f(x) = a^x, then f(r) = a^r, and [f(r)]^s = (a^r)^s = a^rs, by the laws of exponents. Checking the choices:
f(r^s) = a^(r^s), which is not the same as the given.
f(rs) = a^(rs), which is identical to the given.
f(r+s) = a^(r+s), which is not the same.

Therefore the second choice is the correct answer.