$$a^r·a^s = a^{r+s}$$

$${a^r \over {a^s}} = a^{r-s}$$

$$\large({a^r})^s = a^{r·s}$$

$$\large({a·b})^r = a^r·b^r$$

$$\left({a \over b}\right)^r = {a^r \over b^r}$$

$$a^0 = 1$$

$${a^{-r}} = {1 \over a^r}$$

$$\large({a^r})^s = a^{r·s}$$

$$^r\sqrt{a} = a^{1 \over r}$$

$$^s\sqrt{a^r} = a^{r \over s}$$