there is a radicand equation of

1/2n+3=3
There is an index of 4
1/2n +3=3^4
1/2n+3=81
1/2n=78
n=36

You notation is very hard to follow.

Do you mean

[ 1/(2n+3) ]^(1/4) = 3

???

if so
1/(2n+3) = 81
81 (2n + 3) = 1

162 n + 243 = 1

162 n = -242

n = - 1.49