Question

how do you determine 4^1/4 or 4^9/2

Answer 1

Other than by straight definitions it's a little tricky. Although I'd use exponents to see what they are, that is, 4^(1/4)=(4^(1/2))^(1/2), something to the half is sqroot so that's 2^(1/2). For the second =(4^(1/2))^9=2^9=512.

Answer 2

the denom in the exponent is a radical

Answer 3

\[4^{1/4}\text{ means }\sqrt[4]{4}\]

Answer 4

\[4^{9/2}\text{ means }\sqrt{4^9}\]