Negative Exponent Fraction rules?

[bobisaka]

If you look at the screenshot below:
what are the rules in regards to negative exponents?
Does the negative disappear once the exponents has been subtracted?

Why would it not become:

x^-8/4
x^-2
(which would end up being not a real number? x*-x = -x thus -x*-x = x)

 

[Harry_the_cat]

\(\displaystyle \frac{x^a}{x^b} = x^{(a-b)}\)

\(\displaystyle \frac {2}{4} - \frac{-6}{4} = \frac{8}{4}\) NOT \(\displaystyle \frac{-8}{4}\)

 

[Harry_the_cat]

Not sure what you mean by

"x^-2
(which would end up being not a real number? x*-x = -x thus -x*-x = x)"

\(\displaystyle x^{-2} =\frac {1}{x^2}\)

 

[bobisaka]

\(\displaystyle \frac{x^a}{x^b} = x^{(a-b)}\)

\(\displaystyle \frac {2}{4} - \frac{-6}{4} = \frac{8}{4}\) NOT \(\displaystyle \frac{-8}{4}\)

Thanks.