• You do the exponent first, then multiplication.

    -3² = -1 * 3²

    There’s no multiplication, just subtraction (from an unwritten 0). -3² = 0-3²

    there is no space to indicate the - represents a subtraction operator

    Spaces don’t mean anything in Maths, and I don’t know why people keep adding them in! A minus sign is a minus sign, whether there are spaces next to it or not.

    the immediate prefix - actually represents: (-1)x

    No, it actually doesn’t. It represents 0-x. Every operation on the number line starts from 0.

    this actually represents (-1)(x²)

    No, it actually represents 0-x²

    such that PEMDAS is upheld

    Which what you wrote doesn’t. M refers literally to Multiplication signs. S refers literally to subtraction signs. -x² is E then S in PEMDAS.

    I don’t make these rules

    You did make those up actually (or you’ve repeated someone else who made them up).

    but this is how it works

    No it isn’t. A minus sign is the S in PEMDAS, not M.

    Double check in wolfram alpha if you doubt it

    Look in a Maths textbook. Wolfram is known to be wrong in several areas. University professors warn their students against using it without adding brackets everywhere.