Proof that (a/b)^m = (a^m)/(b^m) (where m is an integer)

\((a/b)^m\) basically means:

\[ \overbrace{\frac{a}{b} * \frac{a}{b} * \frac{a}{b} * \ldots}^{m}\]

If we multiply all the fractions:

\[ \frac{\overbrace{a*a*\ldots}^{m}}{\overbrace{b*b*\ldots}^{m}} = \frac{a^m}{b^m}\]

This proves that \( (a/b)^m = (a^m)/(b^m)\). This proof only works when \(m\) is an integer.

Proof That (a/b)^m = (a^m)/(b^m)