Question

the rules for multiplying powers with the same base, dividing powers with the same base, and raising a power to a power?

Answer 1

X is the base
m and m are powers

mulitplying
$(x^m)(x^n)=x^{m+n}$
simply add the powers

dividing
$\frac{x^m}{x^n}=x^{m-n}$
subtract the power on the bottom from the power on top

raising a power
$(x^m)^n=x^{mn}$
multiply the powers