Question

b= 6^30.3^11.7-2^31.5.3^40/2^28.17.3^38-6^27.3^11

Answer 1

\(B=\dfrac{6^{30}\cdot3^{11}\cdot7-2^{31}\cdot5\cdot3^{40}}{2^{28}\cdot17\cdot3^{38}-6^{27}\cdot3^{11}}\)

\(=\dfrac{2^{30}\cdot3^{41}\cdot7-2^{31}\cdot5\cdot3^{40}}{2^{28}\cdot17\cdot3^{38}-2^{27}\cdot3^{38}}\)

\(=\dfrac{2^{30}\cdot3^{40}\left(3\cdot7-2\cdot5\right)}{2^{27}\cdot3^{38}\left(2\cdot17-1\right)}\)

\(=\dfrac{2^3\cdot3^2\cdot\left(21-10\right)}{34-1}=\dfrac{2^3\cdot3^2\cdot11}{33}=\dfrac{2^3\cdot3^2}{3}=2^3\cdot3=24\)