Multiply power with different base?

In order to do this we should use an example such as this:

In order to solve this, we would need to find the solution to (8^4+2a)(16^a-1)

Whenever multiplying two powers and the bases are different, we always want to make the bases the same. We cannot do anything to this equation until the bases are the same, so the equation becomes
(8^4+2a)(16^a-1)-------> (2^3)^4+2a · (2^4)^a-1

Next we multiply the exponent inside with the exponents outside of each pair of brackets and we get  2^12+6a · 2^-4+4a

We have now made the bases the same! And our solution is 2^8+10a