I don't understand how

4root(t cubed) is 4t power (3/2)

√t = t^1/2

why?
because √t*√t = t
t^(1/2) * t^(1/2) = t^(1/2 + 1/2) = t^1 = t

so, √t^3 = (t^3)^(1/2) = t^(3*1/2) = t^(3/2)

nthroot(t) = t^(1/n)
nthroot(t^m) = t^(m/n)