jmc

First, we want to find the relationship between pandas and alpacas. Substituting ``='' for ``as cool as,'' we know that 3 pandas = 7 cats and 2 cats = 5 alpacas. Noting that the lowest common multiple of 2 and 7 is 14, we can multiply the panda-cat equality by 2 to learn that 6 pandas = 14 cats and multiply the cat-alpaca equality by 7 to learn that 14 cats = 35 alpacas. Combining these two equalities, we see that 6 pandas = 35 alpacas. Since $70÷35=2$, we can double the panda-alpaca equation to learn that 12 pandas = 70 alpacas. Therefore, $\boxed{12}$ pandas are as cool as 70 alpacas.

Alternatively, we could set up a string of fractions to ``cancel'' the units: $70\text{ alpacas}\times \frac{2\text{ cats}}{5\text{ alpacas}}\times \frac{3\text{ pandas}}{7\text{ cats}}=\boxed{12}\text{ pandas}$.