Question

[Ngô Hà Duyên]

HELP ME! 

nhanh giúp mik

Answer 1

[Nguyễn Đăng Nhân]

Ta có:

\(\frac{6^{36}\cdot\left(50\cdot5^{40}-10.5^{34}\right)}{30^{30}\cdot10^4\cdot\left(100\cdot15^5-4\cdot3^5\right)}\)

\(=\frac{6^{36}\cdot\left(2^2\cdot5^2\cdot5^{40}-2\cdot5.5^{34}\right)}{30^{30}\cdot10^4\cdot\left(2^2\cdot5^2\cdot3\cdot5-2^2\cdot3^5\right)}\)

\(=\frac{6^{36}\cdot\left(2^2\cdot5^{40+2}-2\cdot5^{34+1}\right)}{30^{30}\cdot10^4\cdot\left(2^2\cdot3\cdot5^{2+1}-4\cdot3^5\right)}\)

\(=\frac{6^{36}\cdot\left(2^2\cdot5^{42}-2\cdot5^{35}\right)}{6^{30}\cdot5^{30}\cdot10^4\cdot\left(2^2\cdot3\cdot5^3-4\cdot3^5\right)}\)

\(=\frac{6^{36-30}\cdot\left[2\cdot\left(2\cdot\left(5^{42}-5^{35}\right)\right)\right]}{5^{30}\cdot10^4\cdot\left(2^2\cdot3\cdot5^3-4\cdot3^5\right)}\)

\(=\frac{2^6\cdot3^6\cdot\left[2\cdot\left(2\cdot5^7\right)\right]}{5^{30}\cdot2^4\cdot5^4\cdot\left[2^2\left(3\cdot5^3-3^5\right)\right]}\)

\(=\frac{2^{6-4}\cdot3^6\cdot\left[2\cdot\left(2\cdot5^7\right)\right]}{5^{30}\cdot5^4\cdot\left[2^2\left(5^3-3^4\right)\right]}\)

\(=\frac{2^2\cdot3^6\cdot2\cdot20^7}{5^{34}\cdot20^3\cdot12^4}\)

\(=\frac{2^3\cdot3^6\cdot20^{7-3}}{5^{34}\cdot12^4}\)

\(=\frac{2^3\cdot3^6\cdot5^4\cdot4^4}{5^{34}\cdot3^4\cdot2^8}\)

\(=\frac{3^2\cdot5\cdot2^8}{5^{30}\cdot2^5}\)

\(=\frac{3^2\cdot2^3}{5^{29}}\)