How to mentaly get answers at once when given in powers?

[dilan]

Is there any method that you can calculate by mentaly and get answers mentaly when a number is given with a power.
I mean for example say, 3^4 will be equal to 81. This is just a simple one. I mean now if a number is given like 6^12 then is there a method that you can get the answer by mental caculation ?

Thank you.

 

[mathman]

This seems to more of a problem in brain function than math. Essentially, how adept are you at multiplying large numbers mentally (I am assuming that you have not memorized a table of logs)? For your example, 6^2=36, 36^2=pa, pa^3=pb. If you can do it, more power to you!

 

[Nimz]

You can sort of cut corners in the process if you memorize powers of numbers. E.g. 6³=216. 6⁴=1296. 6⁵=7776. 6⁶=46656. If you want to do mental calculations of this sort, you can make some sort of tradeoff between what you memorize and what you calculate. I have some of those memorized because I've calculated them several times :P

About 13 years ago a book was written, Dead Reckoning: Calculating Without Instruments, by Ronald W. Doerfler and Ronald E. Doerfler. If you are interested in doing this sort of thing, and more, I'd suggest you take a look at it. Here's the link to it on Amazon.