One basic operator is addition. In order to add the any number x number of times, multiplication was invented. In order to multiply any number x number of times, exponentiation was invented. What if we want to raise a number to a power x number of times? How come we didn't invent that? Also, why is it that addition and multiplication use symbols, but exponents are just simply super-scripted? Why do we have the opposite operations of addition and multiplication but there is no opposite operation of exponentiation? Edit: I realize now that the opposite operation of exponentiation is the radical.