Question

Use the Product Property for Exponents to explain why x · x = x^2.

Answer 1

The Product Property for Exponents is as follows:

$a^b\cdot a^c=a^{b+c}$

So, when we have:

$x\cdot x$

We have no exponents, but actually the exponent is implied to be 1 in this case. So:

$x\cdot x=x^1\cdot x^1$

Now, applying the Product Property for Exponents:

$x\cdot x=x^1\cdot x^1=x^{1+1}=x^2$