Exponents

For $n\in N$ and $a\in R$, $a^n=a\cdot a\cdots a$ ($n$ times, ordinary repeated multiplication). For a negative integer exponent and $a\ne0$, $a^m=\dfrac1{a^{-m}}$ (so $m$ negative flips to a positive power in the denominator). Note $\dfrac aa=a^{1-1}=a^0=1$ for any $a\ne0$.

Properties of exponents (for $m,n\in Z$ and $a\ne0$):

$a^m a^n=a^{m+n},\qquad \dfrac{a^m}{a^n}=a^{m-n}.$ …