When you have a negative exponent, you move the variable with the negative exponent to the other side of the fraction to make the exponent positive.
For example:
[tex]\frac{1}{x^{-3}} =\frac{x^3}{1}[/tex] or x³
[tex]x^{-2}[/tex] or [tex]\frac{x^{-2}}{1} =\frac{1}{x^2}[/tex]
When you multiply a variable with an exponent by a variable with an exponent, you add the exponents together. (The variables have to be the same in order to combine them)
For example:
[tex](y^3)(x^2)=y^3x^2[/tex] (The variables(x and y) are different, so you can't combine them)
[tex](x^3)(x^2)=x^{(3+2)}=x^5[/tex]
[tex]\frac{1}{(y^{-4})(y^2)} =\frac{1}{y^{(-4+2)}} =\frac{1}{y^{-2}} =\frac{y^2}{1}[/tex] or y²
[tex]\frac{7g^{-2}}{g^4}[/tex] First make all the exponents positive
[tex]\frac{7}{g^4(g^2)}[/tex]
[tex]\frac{7}{g^{(4+2)}}[/tex]
[tex]\frac{7}{g^6}[/tex] (This is as far as you can simplify)
