\(=\dfrac{3^6\cdot3^8\cdot5^4-3^3\cdot5^3\cdot5^9}{3^{12}\cdot5^6+3^{12}\cdot5^6}=\dfrac{5^4\cdot3^3\cdot\left(3^{11}-5^8\right)}{3^{12}\cdot5^6\cdot2}=\dfrac{-106739}{3^9\cdot5^2}\)

a)\(\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}=\frac{3^6.\left(3^2.5\right)^4-\left(3.5\right)^{13}.5^{-9}}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}=\frac{3^6.3^8.5^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)

\(=\frac{3^{14}.5^4-3^{13}.5^4}{3^{12}.5^6+3^{12}.5^6}=\frac{3^{13}.5^4.\left(3-1\right)}{3^{12}.5^6\left(1+1\right)}=\frac{3^{13}.5^4}{3^{12}.5^6}=\frac{3}{5^2}=\frac{3}{25}\)

b)\(\frac{4^6.9^5+6^9.120}{-8^4.3^{12}-6^{11}}=\frac{\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.2^3.3.5}{-\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{-2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{-2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{-\left(2^{12}.3^{12}+2^{11}.3^{11}\right)}=\frac{2^{12}.3^{10}\left(1+5\right)}{-\left[2^{11}.3^{11}\left(2.3+1\right)\right]}=\frac{2.6}{-\left(3.7\right)}=\frac{4}{-7}\)

ta có:tử=3^6.45^4-15^3.5^-9

=3^6.15^4.3^4-15^3.5^-9

=3^10.15^4-15^3.5^-9

=3^10.3^4.5^4-5^3.3^3.5^-9

=3^14.5^4-3^3.5^-6

=3^3.5^-6.(3^11.5^10-1)

lam tuong tu vs mau roi rut gon

Ghi rõ đề bài.                 

Ghi rõ đề bài. Cần ghi phân số thì bấn vào fx trên thanh công cụ.

\(\frac{3^6\cdot45^5-15^3\cdot5^9}{27\cdot25^3+45^6}\)

\(=\frac{3^6\cdot3^{10}\cdot5^5-3^3\cdot5^3\cdot5^9}{3^{12}\cdot5^6+5^6\cdot3^{12}}\)

\(=\frac{3^{16}\cdot5^5-3^3\cdot5^{12}}{2\cdot3^{12}\cdot5^6}=\frac{3^3\cdot5^5\left(3^{13}-5^7\right)}{2\cdot3^{12}\cdot5^6}=\frac{3^{13}-5^7}{2\cdot3^9\cdot5}\)

\(=\frac{3^{13}}{2\cdot3^9\cdot5}-\frac{5^7}{2\cdot3^9\cdot5}=\frac{81}{10}-\frac{5^6}{2\cdot3^9}\)

haiz!đến đây tịt!có sai đề ko bạn?

\(A=\frac{3^6.45^5-15^3.5^9}{27^4.25^3+45^6}\)

\(A=\frac{3^6.\left(3^2.5\right)^5-\left(3.5\right)^3.5^9}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}\)

\(A=\frac{3^6.3^{10}.5^5-3^3.5^3.5^9}{3^{12}.5^6+3^{12}.5^6}\)

\(A=\frac{3^{16}.5^5-3^3.5^{12}}{3^{12}.5^6+3^{12}.5^6}\)

\(A=\frac{3^3.5^5.\left(3^{13}-5^7\right)}{2.3^{12}.5^6}\)

\(A=\frac{3^{13}-5^7}{2.3^9.5}\)

Có gì đó sai sai

Sr sr :v Lộn nha :v \(A=\frac{3^6.45^4-15^3.5^9}{27^4.25^3+45^6}\) . Sao lần nào đăng cũng sai đề vậy nhỉ :>

\(=\dfrac{3^6.\left(3^2.5\right)^4-\left(5.3\right)^3.5^{-9}}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}\\ =\dfrac{3^6.3^8.5^4-3^3.5^3.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\\ =\dfrac{3^{14}.5^4-3^3.5^{-6}}{3^{12}.5^6+3^{12}.5^6}\\ =\dfrac{3^3.5^{-6}\left(3^{11}.5^{10}-1\right)}{3^{12}.5^6\left(1+1\right)}\)Hiện mình chỉ làm được đến đây! Để mình suy nghĩ rồi giải tiếp nhé! Chúc bạn học giỏi!!!