Question

Rút gọn các biểu thức sau

A=10.\(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)

Answer 1

\(A=10\cdot\dfrac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)

\(=10\cdot\dfrac{\left(2^2\right)^6\cdot\left(3^2\right)^5+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{\left(2^3\right)^4\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=10\cdot\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=10\cdot\dfrac{2^{12}\cdot3^{10}\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}\)

\(=10\cdot\dfrac{2\cdot6}{3\cdot5}\)

\(=10\cdot\dfrac{12}{15}=10\cdot\dfrac{4}{5}\)

\(=8\)