Hi Yuhai,
The problem is that Subsuperscript is just notation, there is no Power in the expression. Use Power instead.
eq = 1/4 Subscript[n, 1]^4 + 1/2 Subscript[n, 2]^2 Subscript[n, 1]^2 + 1/4 Subscript[n, 2]^4
Simplify@eq
$$\frac{1}{4} \left(n_1^2+n_2^2\right){}^2$$
