When you multiply a base with an exponent by a base with an exponent, you add the exponents together. (But you can only combine the exponents when the bases are the same)
For example:
[tex]x^3(x^1)=x^{(3+1)}=x^4[/tex] (they have the same base of x)
[tex]y^3(x^2)=y^3x^2[/tex] (you can't combine the exponents because they have different bases of y and x)
[tex]2^2(2^1)=2^{(2+1)}=2^3=8[/tex]
When you have a negative exponent, you move the base with the negative exponent to the other side of the fraction to make the exponent positive.
For example:
[tex]x^{-3}[/tex] or [tex]\frac{x^{-3}}{1} =\frac{1}{x^3}[/tex]
[tex]\frac{1}{y^{-2}} =\frac{y^2}{1}[/tex] or [tex]y^{2}[/tex]
[tex]7^3*7^{-5}[/tex] Add the exponents together
[tex]7^{(3+(-5))}[/tex]
[tex]7^{-2}[/tex] Make the exponent positive
[tex]\frac{1}{7^2}[/tex] Simplify
[tex]\frac{1}{49}[/tex]
