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Diffie-Hellman key exchange is a really cool trick and this video explains it clearly in 2'18"

Perhaps it needs to be longer, adding that (a^b)^c is the tiny number and a^(b^c) is the huge number. Diffie-Hellman uses the tiny number because it is a bit lame (a^b)^c = a^(b times c) = a^(c times b) = (a^c)^b

I like to make my examples with Common Lisp, because the fully parenthesised prefix notation makes things explicit. No stubbing by toe on what 3^5^7 actually means.

(expt (expt 3 5) 7) => 50031545098999707

(expt (expt 3 7) 5) => 50031545098999707

(expt 3 (* 5 7)) => 50031545098999707

(expt 3 (expt 5 7)) has 37276 decimal digits