Question

Answer 1

b: \(=\dfrac{2^{74}\left(2^2-1\right)}{2^{76}\left(2^2-1\right)}=\dfrac{1}{2^2}=\dfrac{1}{4}\)

c: \(=\dfrac{12\left(2\cdot6+6\cdot20+21\cdot32\right)}{9\cdot8\left(5+2\cdot25+2\cdot14\cdot5\right)}=\dfrac{1}{6}\cdot\dfrac{268}{65}=\dfrac{134}{195}\)

Answer 2

b) \(\dfrac{2^{76}-2^{74}}{2^{78}-2^{76}}=\dfrac{2^{74}\cdot\left(2^2-1\right)}{2^{76}\cdot\left(2^2-1\right)}=\dfrac{2^{74}}{2^{76}}=\dfrac{1}{2^2}=\dfrac{1}{4}\)