exp(60_deg) would be the way to raise e to the 60-degrees power, but that generates an error because it doesn't make any sense.
If what you're trying to do is convert the vector "100 units at 60 degrees" from polar notation to rectangular notation, just set degree mode and type 100 [angle] 60 Enter, then press the [angle] key again, and you'll see the result shown below. (The angle symbol is keyed by pressing Shift multiply).
Converting from rectangular to polar can also be done the same way.
Disclaimer: I don't work for HP, but HP calculators work for me.