## Vibhor16 3 years ago Is there an easy way to mentally calculate 2^n (where n can be any natural no.)?

1. experimentX

memory 1 2 4 8 16 32 64 128 256 512 1024 ...

1?

3. experimentX

2^0

0 is not a natural no

5. experimentX

some include 0 as natural number while some do not http://en.wikipedia.org/wiki/Natural_number

6. Vibhor16

what about 54,55,56,... you can't just memories them all !

7. experimentX
8. experimentX

the best way is to memorize up to 2^10 ... or 2^something ... then multiply it by two until your you get your result.

Use the calculator \[x ^{y}\] button.

why would you ever need 2^54 or something that large?

11. experimentX

I realize that is not really a "mentally" way, but when you get above 2^7 that would be the way I would do it mentally.

use the tools.

14. SMISHRA

@experimentX , 0 can not be an element of N.

15. experimentX

I looked into wikipedia .... it said that 0 is still debated as it is an element of N or not

16. experimentX

besides ... the question hardly focuses on 0 is a natural number or not ... and i'm in no position to argue that

17. satellite73

any natural number at all? seems doubtful since this grows very large very fact. but i count on my fingers, doubling each time two four eight sixteen thirty two sixty four one twenty eight two fifty six five twelve ten twenty four it helps to be old an remember when a computer actually came with one twenty eight two fifty six or five twelve megs, so those numbers are familiar.