Logic problem: Truth value of statement the product of $x^2$ and $x^3$ is $x^6$

Question

I want to understand why these statements below are false. I assumed that the statements are true because they are real numbers

• The product of $x^2$ and $x^3$ is $x^6$
• The $x^2>0$ for any real number $x$

Answer 1

• The product of $x^2$ and $x^3$ is $x^6$

Do you know a rule for $\boxed{x^m x^n = \ldots}$ ?

Don't confuse it with the rule for $\boxed{\left(x^m\right)^n = \ldots}$ !

If not, look them up.

• The $x^2>0$ for any real number $x$

But also $0$ is a real number, so...