Question

a) \(\frac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}\) 

b) (1+2+3+4+....+100)x(\(1^2\) +\(2^2\) \(3^2\) +....+\(10^2\) )x(65 x 111 -13x15x37)

Answer 1

a.

\(\frac{2^{10}\times13+2^{10}\times65}{2^8\times104}=\frac{2^{10}\times\left(13+65\right)}{2^8\times104}=\frac{2^2\times78}{104}=\frac{4\times78}{104}=\frac{312}{104}=3\)

b.

\(\left(1+2+...+100\right)\times\left(1^2+2^2+...+10^2\right)\times\left(65\times111-15\times37\times13\right)\)

\(=\left(1+2+...+100\right)\times\left(1^2+2^2+...+10^2\right)\times\left(7215-7215\right)\)

\(=\left(1+2+...+100\right)\times\left(1^2+2^2+...+10^2\right)\times0\)

= 0

 

Answer 2

a. 3

b. 0