(999)4 can be written as(1000 - 1)4
.
=(1000 - 1)4
= 4C0 (1000)4 - 4C1(1000)3+4C2 (1000)2 - 4C3 (1000)1 + 4C4
.
= 1(1000)4-4 (1000)3+6(1000)2-4(1000)1+ 1
= [ (1000,000,000,000) - (4,000,000,000) ] + [ (6,000,000) - (4,000) + 1 ]
= [ 996,000,000,000 ] + [6,004,001 ]
= 996,006,004,001
.
Hence (999)4=996,006,004,001
.
