$\left(\dfrac{a^{m}}{a^{n}}\right)^{p}$ equals

$\left(\dfrac{a^{m}}{a^{n}}\right)^{p}$ equals
  1. $a^{(m-n)p}$
  2. $a^{m-n+p}$
  3. $a^{m-np}$
  4. $a^{mp-n}$

Solution

$\dfrac{a^{m}}{a^{n}} = a^{m-n}$, then raised to $p$ gives $a^{(m-n) \cdot p}$.

Asked in: IMO

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