Thread: Too big for TI-84

I need to calculate e to the 408 and my calculator reads overflow after e to the 200. How do you solve. The text answer is 1.65 X 10 to the 177!!
But I need to be able to solve a similar problem on a test.

Originally Posted by dclivefree

I need to calculate e to the 408 and my calculator reads overflow after e to the 200. How do you solve. The text answer is 1.65 X 10 to the 177!!
But I need to be able to solve a similar problem on a test.

e^408 = (e^102)^4.

e^102 = 1.9862648 X 10^44.

Therefore e^408 = (1.9862648 X 10^44)^4 = (1.9862648)^4 X 10^176.

(1.9862648)^4 = 15.56498 = 1.556 X 10.

Therefore e^408 = 1.556 X 10 X 10^176 = 1.56 X 10^177 (to two significant figures).

p.s. Obviously I have a slight disagreement with the text answer.