From the documentation on MDN:
In JavaScript, it is impossible to write an ambiguous exponentiation expression, i.e. you cannot put a unary operator (+/-/~/!/delete/void/typeof) immediately before the base number.
The reason is also explained in that same text:
In most languages like PHP and Python and others that have an exponentiation operator (typically ^ or **), the exponentiation operator is defined to have a higher precedence than unary operators such as unary + and unary -, but there are a few exceptions. For example, in Bash the ** operator is defined to have a lower precedence than unary operators. 
So to avoid confusion it was decided that the code must remove the ambiguity and explicitly put the parentheses:
(-1)**2
or:
-(1**2) 
As a side note, the binary - is not treated that way -- having lower precedence -- and so the last expression has the same result as this valid expression:
0-1**2
Exponentiation Precedence in Other Programming Languages
As already affirmed in above quote, most programming languages that have an infix exponentiation operator, give a higher precedence to that operator than to the unary minus. 
Here are some other examples of programming languages that give a higher precedence to the unary minus operator: