It’s written as - (n^2). The sign in outside

First one. There's actually no need for the brackets

if n = 4,

-n² = -4²
= -16


Second one is (-n)² = -n x -n

= n²

Basically the square comes before the negative sign, so

-n^2 means
- of (n x n)

but (-n)^2 means
(-n) times (-n)
and the two negatives cancel each other.

Order of operations is

Brackets
Powers
Division/multiplication, whichever comes first in the line
Addition/subtraction, whichever comes first in the line

For -n², the exponent/power is done first so when n = 4,

-n² = - 4²
= -16

However, if n is negative instead, you need to put brackets since the squaring applies to the negative as well.

Eg. If n = -3,

Then -n²
= -(-3)²
= -(-3 x -3)
= -(3 x 3)
= -9

It would be incorrect to write
-(-3²)
= -(-9)
= 9