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

1 Answer
Oct 5, 2015

Answer:

#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#