what is 56,890,234,000 to the 5th power?

Question

My collage teacher threw that at us and told us to answer with out a caculater he never said any thing about the internet.......

Answer 1

Well if you factor it you get:
56,890,234,000 = 28,445,117 x 2,000

If you take this to the 5th power you have:
28,445,117^5 x 2^5 x 1,000^5

28,445,117^5 x 32 x 10^3^5
= 28,445,117^5 x 32 x 10^15

As far as I can tell 28,445,117 is prime, so I don't see an easy way to do this without multiplying by hand now...

It might be helpful to write down the multiples of 28,445,117:
1 x 28,445,117 = 28,445,117
2 x 28,445,117 = 56,890,234
3 x 28,445,117 = 85,335,351
4 x 28,445,117 = 113,780,468
5 x 28,445,117 = 142,225,585
6 x 28,445,117 = 170,670,702
7 x 28,445,117 = 199,115,819
8 x 28,445,117 = 227,560,936
9 x 28,445,117 = 256,006,053

So to square you would have:
20,000,000: 568,902,340,000,000
8,000,000: 227,560,936,000,000
400,000: 11,378,046,800,000
40,000: 1,137,804,680,000
5,000: 142,225,585,000
100: 2,844,511,700
10: 284,451,170
7: 199,115,819

Add that up by hand and you have:
28,445,117² = 809,124,681,143,689.

Repeat another time and you get:
28,445,117^3 = 23,015,646,222, 719,927,416,613

Repeat again and you get:
28,445,117^4 = 654,682,749,635,876, 393,597,064,528,721

Repeat one final time and you get:
28,445,117^5 = 18,622,527,411,274, 211,413,406,551, 376,018,705,357

Finally multiply by 32:
30: 558,675,822,338,226, 342,402,196,541, 280,561,160,710
2: 37,245,054,822,548, 422,826,813,102, 752,037,410,714

Add these together:
595,920,877,160, 774,765,229,009, 644,032,598,571,424

Finally add the 15 trailing zeroes.
595,920,877,160,774, 765,229,009,644, 032,598,571,424, 000,000,000,000,000

I think that's it without resorting to a calculator or a computer.

Answer 2

No regular calculator could give the exact answer anyway. If there's a trick to doing this calculation, I don't know what it is.

A symbolic algebra program like Mathematica or Maple could do the exact multiplication. Most computers using Unix/Linux have an application named bc which can do such as well. The answer, according to bc, is

5959208771607747652290096440
32598571424000000000000000

(I had to split it into two lines for the whole thing to show...)