a) \(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4.\left(5.2^2\right)^4}{\left(5^2\right)^5.\left(2^2\right)^5}=\frac{5^4.5^4.2^8}{5^{10}.2^{10}}=\frac{5^8.2^8}{5^{10}.2^{10}}=\frac{1}{5^2.2^2}=\frac{1}{25.4}=\frac{1}{100}.\)

Chúc bạn học tốt!

Đề bài yêu cầu gì?

Ta có: \(\frac{\frac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}}{\sqrt{\frac{25}{9}}}=\frac{\frac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+3^8\cdot2^8\cdot20}}{\frac{5}{3}}=\frac{2^{10}\left(3^8-3^9\right)}{2^83^8\left(2^2+20\right)}\cdot\frac{3}{5}=\frac{2^83^8\left(1-3\right)\cdot2^2}{2^83^8\cdot24}\cdot\frac{3}{5}\)

\(=\frac{-2\cdot2^2}{24}\cdot\frac{3}{5}=\frac{-8}{24}\cdot\frac{3}{5}=\frac{-24}{120}=\frac{-1}{5}\)

\(\frac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}:\sqrt{\frac{25}{9}}\\ =\frac{2^{10}\cdot3^8-2\cdot\left(2\cdot3\right)^9}{2^{10}\cdot3^8+\left(2\cdot3\right)^8\cdot\left(2^2\cdot5\right)}:\frac{5}{3}\\ =\frac{2^{10}\cdot3^8-2\cdot2^9\cdot3^9}{2^{10}\cdot3^8+2^8\cdot3^8\cdot2^2\cdot5}\cdot\frac{3}{5}\\ =\frac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}\cdot\frac{3}{5}\\ =\frac{2^{10}\cdot3^8\left(1-3\right)}{2^{10}\cdot3^8\left(1+5\right)}\cdot\frac{3}{5}\\ =\frac{1-3}{1+5}\cdot\frac{3}{5}\\ =\frac{-2}{6}\cdot\frac{3}{5}=\frac{-1}{5}\)

\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)

=\(\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.5.3^8}=\frac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}=-\frac{2}{6}=-\frac{1}{3}\)

Bằng 1/6

A=2¹⁰.3¹⁰-2¹⁰.3⁹/2¹⁰.3⁸+2¹⁰.3⁸.5

A=2^10.3^9(1.3-1.1)/2^10.3^8(1.1+1.1.5)

A=3.2/1.6

A=6/6=1

\(E=\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)

\(E=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.6^9}{2^{10}.3^8+6^8.2^2.5}\)

\(E=\frac{2^{10}.3^8-2.6^9}{2^{10}.3^8+6^8.2^2.5}\)

\(E=\frac{-6}{10}\)

\(E=\frac{-3}{5}\)

vay \(E=\frac{-3}{5}\)

Kết quả cô mik cho là \(\frac{-1}{3}\)cơ !

\(E=\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)

\(E=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2\left(2.3\right)^9}{2^{10}.3^8+6^8.2^2.5}\)

\(E=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)

\(E=\frac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}\)

\(E=\frac{-2}{6}=\frac{-1}{3}\)

MK CHẮC CHẮN ĐÚNG

\(=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^8.2^2.5}=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}=\frac{2^{10}.\left[3^8.\left(1-8\right)\right]}{2^{10}.3^8.\left(1+5\right)}=\frac{2^{10}.3^8.\left(-7\right)}{2^{10}.3^8.6}=\frac{-7}{6}\)