( x^{m})(x^{n}) =   x^{m+n} , which means when your operation is multiplication addition of exponents.
 \frac{ x^{m}}{x^{n}} =  x^{m-n} , which means when the operation is division subtract the exponents.
 xy^{2} =x^{2} y^{2}  , which means when the operation is multiplication and your bases are not the same (like variable and numbers) just raise it by the exponent given. (Same with fraction/division).
 (x^{m})^{n}  =  x^{mn} , which means the exponents are inside and outside the parentheses it should be multiplied.

Hope I helped. That's not all :)