Starting with the given equations:
s^2 = t^-1
t^(1/4) = u^(-1/3)
First, we can simplify the second equation by raising both sides to the 4th power:
t^(1/4)^4 = u^(-1/3)^4
t = u^(-4/3)
Substitute this value for t in the first equation:
s^2 = (u^(-4/3))^-1
s^2 = u^(4/3)
Taking the square root of both sides:
s = ± u^(2/3)
Therefore, the value of s in terms of u is s = ± u^(2/3).