1) We need to consider that whenever we have a variable its exponent is raised to the 1st power, even when we don't write it as a superscript.
2) So we can write out the following steps to get that product as x²:
[tex]\begin{gathered} x=x^1 \\ x^1\cdot x^1=x^{1+1}=x^2 \end{gathered}[/tex]That's why we can write that, applying the property of exponents.
