\(x^m * x^n\) basically means:
\[ \overbrace{x*x*\ldots}^{m} * \overbrace{x*x*\ldots}^{n} \]
Together this means:
\[ \overbrace{x*x*x*\ldots}^{m+n} \]
This means \(x^m * x^n = x^{m+n}\). This proof only works when \(m\) and \(n\) are integers.
\(x^m * x^n\) basically means:
Together this means:
This means \(x^m * x^n = x^{m+n}\). This proof only works when \(m\) and \(n\) are integers.