Question

a, B=\(\dfrac{2^{10}.13+2^{10}.65}{2^8.104}\) b, C=\(\dfrac{4^9.36+64^9}{16^4.100}\)

c, D=\(\dfrac{72^3.54^2}{108^4}\) d, E=\(\dfrac{4^6.3^4.9^5}{6^{12}}\)

Answer 1

a, \(B=\dfrac{2^{10}.13+2^{10}.65}{2^8.104}\)

\(=\dfrac{2^{10}.\left(13+65\right)}{2^8.2^3.13}\)

\(=\dfrac{2^{10}.78}{2^{11}.13}\)\(=\dfrac{1.6}{2.1}=\dfrac{1.3}{1.1}=3\)

Answer 2

b: \(=\dfrac{2^{20}\cdot3^2+2^{54}}{2^{18}\cdot5^2}=\dfrac{2^{20}\left(3^2+2^{32}\right)}{2^{18}\cdot5^2}=\dfrac{2^2\left(3^2+2^{32}\right)}{25}\)

c: \(=\dfrac{2^9\cdot3^6\cdot3^6\cdot2^2}{2^8\cdot3^{12}}=\dfrac{2^{11}}{2^8}=8\)

d: \(=\dfrac{2^{12}\cdot3^4\cdot3^{10}}{2^{12}\cdot3^{12}}=9\)