Public Key Cryptography: Diffie-Hellman Key Exchange Please watch this video it's very short. If you already know cryptography and really good at it please start from 3:51.

I didn't understand the step at 4:39, can someone here to explain? 

Why is $16^{54} \mod 17$ is equal to

$3 ^ {24\times54} \mod17 \equiv 1$?

He just wrote that. Alice didn't knew bob's private number how did he raised $3 ^{24}$?
Alice didn't know that $16\equiv 3^{24}\mod 17$. The video just made it clearer that they were intrisically computing the same value.

I'm guessing that the point the video was trying to make was that 
$$3^{54\times24}\equiv3^{24\times54}\equiv 16^{54}\equiv15^{24}\equiv1\mod 17.$$