Question -
Answer -
(i) (96)3
We have,
(96)3
Let us express thegiven expression as two different entities and apply the binomial theorem.
(96)3 =(100 – 4)3
= 3C0 (100)3 (4)0 – 3C1 (100)2 (4)1 + 3C2 (100)1 (4)2 – 3C3 (100)0 (4)3
= 1000000 – 120000 +4800 – 64
= 884736
(ii) (102)5
We have,
(102)5
Let us express thegiven expression as two different entities and apply the binomial theorem.
(102)5 =(100 + 2)5
= 5C0 (100)5 (2)0 + 5C1 (100)4 (2)1 + 5C2 (100)3 (2)2 + 5C3 (100)2 (2)3 + 5C4 (100)1 (2)4 + 5C5 (100)0 (2)5
= 10000000000 +1000000000 + 40000000 + 800000 + 8000 + 32
= 11040808032
(iii) (101)4
We have,
(101)4
Let us express thegiven expression as two different entities and apply the binomial theorem.
(101)4 =(100 + 1)4
= 4C0 (100)4 + 4C1 (100)3 + 4C2 (100)2 + 4C3 (100)1 + 4C4 (100)0
= 100000000 + 4000000+ 60000 + 400 + 1
= 104060401
(iv) (98)5
We have,
(98)5
Let us express thegiven expression as two different entities and apply the binomial theorem.
(98)5 =(100 – 2)5
= 5C0 (100)5 (2)0 – 5C1 (100)4 (2)1 + 5C2 (100)3 (2)2 – 5C3 (100)2 (2)3 + 5C4 (100)1 (2)4 – 5C5 (100)0 (2)5
= 10000000000 –1000000000 + 40000000 – 800000 + 8000 – 32
= 9039207968