We have, 102 = 100 + 2
∴ (102)5 = (100+2)5
=

5

‌

C0(100)5+

5

‌

C1(100)4(2) +

5

‌

C2(100)3(2)2+

5

‌

C3(100)2(2)3 +

5

‌

C4(100)(2)4+

5

‌

C5(2)5
= (100)5+5(100)4(2) + 10(100)3(4)+10(100)2(8) + 5 (100) (16) + 1 (32)
= 10000000000 + 1000000000 + 40000000 + 800000 + 8000 + 32
= 11040808032.