Math CentralQuandaries & Queries


Question from Dan, a student:

I would like to know how to calculate a whole number as the base that
has a large exponent;Such as 7 to the 23rd.power=. Otherwise if I use a calculator
it goes off the scale.
Thanks,hope you can help.

Hi Dan. If this is pre-algebra, then just multiply 7 by 7 and keep
multiplying until you go off the scale of your calculator (keep track of
how many 7s you have used up). Write the values down as you go.

Then break down your problem into pieces of that size or smaller.

Now turn to pen and paper to complete it.

Here's an example. I want to calculate 622 using my 8-digit calculator.

First I use my calculator to see how far I get before it runs out of room:
6 x 6 = 36
x 6 = 216
x 6 = 1296
x 6 = 7776
x 6 = 46656
x 6 = 279936
x 6 = 1679616
x 6 = 10077696
x 6 = 60466176
(too big)

So I got to 60466176 using 10 sixes. So 610 = 60466176.

Remember the rules of exponents. 622 = 62 x 610 x 610. That breaks it down into smaller pieces.

So that means 622 = 36 x 60466176 x 60466176

Now I turn to pen and paper to multiply the final result by hand (carefully!)

I get 131621703842267136.

Now you can try with 723.

Hope this helps,
Stephen La Rocque.

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