Question

Compute $(98{)}^5$.

• A. $9039007948$
• B. $9039207968$
• C. $9029007968$
• D. $9049007698$

Answer 1

Answer: (B)

We have $(98{)}^5=(100-2{)}^5$
$={}^5{C}_0(100{)}^5-{}^5{C}_1(100{)}^4\cdot 2+{}^5{C}_2(100{)}^3{2}^2-{}^5{C}_3(100{)}^2(2{)}^3$
$+{}^5{C}_4(100)(2{)}^4-{}^5{C}_5(2{)}^5$
$=10000000000-(5\times 100000000\times 2)+(10\times 1000000\times 4)$
$-(10\times 10000\times 8)+(5\times 100\times 16)-32$
$=10040008000-1000800032$
$=9039207968$.