Question

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

Answer 1

`x^1\cdot x^1=x^(1+1)=x^2`

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:

`\begin{gathered} x=x^1 \\ x^1\cdot x^1=x^(1+1)=x^2 \end{gathered}`

That's why we can write that, applying the property of exponents.