Simplify each expression. x y ⋅ 3 x 2 xy\cdot3x^2

For this problem, we want to simplify the expression x times y times three times x squared. And we're going to use the product rule. Now first, it might not look like we can apply the product rule since our term x times y and three times x squared don't have the same base. But first, we're going to break apart these terms to see that we do have certain terms within our terms that do have a common base. So let's first look at this by rewriting it as x times y times three times x squared. Now, do any of these terms have a common base? Yes. Our x and our x squared. So we can go ahead and combine those two terms using our product rule. And doing that, we get x to the one plus two power, which is three, times y times three. And this is our expression written in its simplest form.