When we find the product of two terms that has the same base (in this case, a), we can simply add the powers. This can be explained using knowledge of squares and cubed. __a__^{2 }= a x a and __a__^{3} = a x a x a and so if we want to find a^{2 }x a^{3} then we can write **a x a x a x a x a**. This is also the same as a^{5} and therefore I have proved why we can add the powers when we multiply two terms with the same base.