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One way to view the exponent, especially when it is a natural number, is how many times something need to be multiplied by itself. So 4^5 has exponent 5 and base 4 and it means 4 multiplied by itself 5 times, ie 4x4x4x4x4 We can then extent this to negative integers and to an exponent of zero and then to rational exponents. More on that if you want to know.

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