I don't know. I am assuming that your maths teacher knows that you can't do that sum on a standard calculator and is expecting you to use some maths to work out this answer. How about:

2^10 = 1024

so 2^10000 = 1024^1000
= 1000^1000 x 1.024^1000
= 10^3000 x 1.024^1000

Now 1.024^1000 can be done on a normal calculator. It equals 2.00 x 10^10 to 3 sig. fig..

Therefore 2^10000 = 2.00 x 10^3010 calculated on a normal calculator using a little ingenuity.