Show me why the product of a squared and a cubed is a to the power of 5.

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. a² = a x a and a³ = a x a x a and so if we want to find a² x a³ then we can write a x a x a x a x a. This is also the same as a⁵ and therefore I have proved why we can add the powers when we multiply two terms with the same base.