Question

The value of the expression $\frac{1+4.343+7.4+2.3.49+7.343}{16+2^6.3^1+2^5.3^3+2^6.3^3+2^4.3^4}$ equal

• A. $1$
• B. $2$
• C. $4$
• D. $3$

Answer 1

The correct option is A $1$

$\frac{1+4.343+7.4+2.3.49+7.343}{16+2^6.3^1+2^5.3^3+2^6.3^3+2^4.3^4}$

Above expression can be written as

$\frac{{}^4{C}_0\cdot 1^4+{}^4{C}_1\cdot 1^3\cdot 7+{}^4{C}_2\cdot 1^2\cdot 7^2+{}^4{C}_3\cdot 1\cdot 7^3+{}^4{C}_4\cdot 7^4}{{}^4{C}_0\cdot 2^4+{}^4{C}_1\cdot 2^3\cdot 6+{}^4{C}_2\cdot 2^2\cdot 6^2+{}^4{C}_3\cdot 2\cdot 6^3+{}^4{C}_4\cdot 6^4}$

$=\frac{(1+7{)}^4}{(2+6{)}^4}=1$