Please explain how to answer the following:a^4/a^r

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Think of it as a^4*(1/a^r). We can simplify 1/a^r to a^(-r), giving us a^4*a^(-r). When we multiply exponential terms and they have the same base, a, we add the exponents, giving us a^(4+-r) or a^(4-r). You can generalize this to show that when you divide exponential terms and they have the same base you subtract the exponents.