Question

How do you simplify `5^25 - 5^3`?

Answer 1

`5^25-5^3 = 298023223876953125 - 125 = 298023223876953000`

Explanation:

How do we find `5^25 = 298023223876953125` ?

The obvious way is to start with `1` and multiply it by `5`, `25` times.

I prefer to start with `10^25 = 10000000000000000000000000` and divide it by `2`, `25` times...

`10000000000000000000000000`
`color(white)(0)5000000000000000000000000`
`color(white)(0)2500000000000000000000000`
`color(white)(0)1250000000000000000000000`
`color(white)(00)625000000000000000000000`
`color(white)(00)312500000000000000000000`
`color(white)(00)156250000000000000000000`
`color(white)(000)78125000000000000000000`
`color(white)(000)39062500000000000000000`
`color(white)(000)19531250000000000000000`
`color(white)(0000)9765625000000000000000`
`color(white)(0000)4882812500000000000000`
`color(white)(0000)2441406250000000000000`
`color(white)(0000)1220703125000000000000`
`color(white)(00000)610351562500000000000`
`color(white)(00000)305175781250000000000`
`color(white)(00000)152587890625000000000`
`color(white)(000000)76293945312500000000`
`color(white)(000000)38146972656250000000`
`color(white)(000000)19073486328125000000`
`color(white)(0000000)9536743164062500000`
`color(white)(0000000)4768371582031250000`
`color(white)(0000000)2384185791015625000`
`color(white)(0000000)1192092895507812500`
`color(white)(00000000)596046447753906250`
`color(white)(00000000)298023223876953125`