Question

Rút gọn biểu thức: A=\(\dfrac{12^{10}.35+2^{10}.65+6^2.12^6.15^2}{2^8.10^4}\)

Answer 1

\(A=\dfrac{2^{20}\cdot3^{10}\cdot35+2^{10}\cdot65+2^2\cdot3^2\cdot2^{12}\cdot3^6\cdot3^2\cdot5^2}{2^{12}\cdot5^4}\)

\(=\dfrac{2^{10}\left(2^{10}\cdot3^{10}\cdot35+65+2^4\cdot3^{10}\cdot5^2\right)}{2^{12}\cdot5^4}\)

\(=\dfrac{1}{4}\cdot\dfrac{2^4\cdot3^{10}\cdot5\cdot\left(2^6\cdot7+5\right)+65}{5^4}\)

\(=\dfrac{1}{4}\cdot\dfrac{2^4\cdot3^{11}\cdot5\cdot151+65}{5^4}\)

\(=\dfrac{1}{4}\cdot\dfrac{2^4\cdot3^{11}\cdot151+13}{5^3}=\dfrac{2^4\cdot3^{11}\cdot151+13}{500}\)