   SEARCH HOME Math Central Quandaries & Queries  Question from cecil, a student: what is the exponent form 564000? Hi Cecil. If you break it down into its prime factors then you can see how many times each factor appears. This becomes its exponent form. For example if I start with 1258600:

100 goes into 1258600:
1258600 = 12586 x 100.

2 goes into 12586:
1258600 = 2 x 6293 x 100

7 goes into 6293:
1258600 = 2 x 7 x 899 x 100

29 goes into 899:
1258600 = 2 x 7 x 29 x 31 x 100

100 is 2 x 5 x 2 x 5:
1258600 = 2 x 7 x 29 x 31 x 2 x 5 x 2 x 5

All these are prime factors. 2 appears three times, so we make its exponent a 3. As well, 5 appears twice, so we make its exponent a 2. The others appear just once each, so we don't write the exponent. When it isn't written, the exponent is a 1, which is what we want:
1258600 = 2³ x 5² x 7 x 29 x 31.

That's the exponent form for 1258600. Try your number the same way.

Cheers,
Stephen La Rocque.

Cecil,

If you mean to write the number in scientific notation then, for example Stephen's number 1258600, written in scientific notation is 1.2586 × 106.

Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.