Playing With e & pi

1. What is e^(pi)?

2. What is pi^e)?

Can this be calculated without a calculator?

 

No, both e and pi are irrational numbers. With or without a calculator, e^pi and pi^e can only be approximated.

If you really, really want to do them withouut a calculator, approximate e as 2.72 and pi as 3.14. e^pi is approximately 2.72^(3.14)= (2.72^3)(2.72^0.14). 2.72^3 is (relatively) easy. 2.72^0.14= 2.72^(14/100)= 2.72^(7/50)= (2.72^7)^(1/50). 2.72^7 is (relatively) easy. To find that to the 1/50= (1/2)(1/25), first take its square root. To find the 25th root= fifth root of fifth root, take the fifth root of the fifth root.

I believe I could do that but it would take me several days so I think I will use a calculator- that's what they were invented for! (You could WALK from Moscow to Paris in the dead of winter but I believe I would take an airplane!)

 

Ok. Cool. We can only get an approximation.