There is something known as the Law of Exponents. There are many forms of it, but we are using only 2 of them, the Product Rule and the Quotient Rule. The Product Rule indicates that x^a*x^b=x^a+b. The Quotient Rule indicates that x^a/x^b=x^a-b. Solution A is correct because 5^5*5^7/5^13 = 5^5+7-13=5^-1 or 1/5. Solution B is correct because 5^5+7+(-13) = 5^-1 or 1/5. Solution C is correct because 5^12-13=5^-1 or 1/5. Solution D is correct because 5^5+7-13=5^-1 or 1/5. If you are confused at all, don't hesitate to ask questions.