Exponent Rules Question

As I’m getting familiar with the exponent rules, I’m coming across a contradicting rule where they say, negative#^anything = negative#. However, I came across another question stating “How many real values of x exist such that x^2 = -49?” According to the first concept wouldn’t it be one value because -7^2 = -49, but the answer was 0. Can someone please explain. thank you.

I’d be happy to explain it further if I didn’t really make sense there.

You should consider sketching y = x^2 and y = -49

Yes, I know that y = x^2 has a parabola shape and y = -49 is a linear shape. So are you saying that the concept of “negative#^anything = negative#” is not true?

No, my point is that y = x^2 is never negative.

I think you’re confusing -x^2 with (-x)^2

Yea I’m having trouble wrapping my head around that concept because x^2 = 81, can also be both 9 or -9. So you see how it contradicts when you say y = x^2 can never be negative.

“y = x^2 is never negative” means y is never negative. x can be anything in this case because there’s no restriction against any value(s) of x.

I seeeee. I think its starting click. Thanks for the help!