The Product Property for Exponents is as follows:
[tex]a^b\cdot a^c=a^{b+c}[/tex]So, when we have:
[tex]x\cdot x[/tex]We have no exponents, but actually the exponent is implied to be 1 in this case. So:
[tex]x\cdot x=x^1\cdot x^1[/tex]Now, applying the Product Property for Exponents:
[tex]x\cdot x=x^1\cdot x^1=x^{1+1}=x^2[/tex]