# Large indeces to standard form

• Sep 12th 2011, 02:24 PM
mabentley
Large indeces to standard form
Hello everyone,

Please could someone suggest how I can convert the following into standard form using algebra:

$\displaystyle 3^{376}$
• Sep 12th 2011, 02:32 PM
pickslides
Re: Large indeces to standard form
You want the numeral for this power representation?

Well $\displaystyle 3^{376} = 3^{2\times 188} = 9^{188} = 9^{2\times 94} = 81^{94} = \dots$
• Sep 12th 2011, 02:47 PM
mabentley
Re: Large indeces to standard form
Thanks for the reply. I need not just the numeral but standard form:

m x 10^n
• Sep 12th 2011, 02:52 PM
pickslides
Re: Large indeces to standard form
Okay, well the bad news is the basic numeral is a really really big number.

Do you have to show your working or do you just need to know?

Using technology $\displaystyle 3^{376}\approx 2.498\times 10^{179}$
• Sep 12th 2011, 03:03 PM
mabentley
Re: Large indeces to standard form
It's an example question from an A-level paper - so I'd be allowed a standard calculator. I'd be surprised if my calculator could make the approximation above, so I was expecting there would be an algebraic method of some sort...

Thanks again.