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Positive and negative numbers with exponents

One of the most commonly seen errors when raising a base by its exponent has to do with the application of the negative symbol to the exponent. For example, what is the difference between (-3)^2 and -3^2? In the first case, -3 is squared by itself. In other words, (-3)^2 = -3 x -3. The answer is 9. In the latter case, we first square three. It is only after we do this that we apply the negative sign. Therefore, in the latter case, we simply multiply 3 by 3 and then add the negative sign. Our answer will be -9. The function of the parentheses in the first case is to specify that the negative sign functions as a component of the base which is multiplied.