\(\frac{5^4\cdot20^4}{25^5\cdot4^5}=\frac{5^4\cdot5^4\cdot4^4}{5^5\cdot5^5\cdot4^5}=\frac{1}{100}\)

=\(\frac{100^4}{100^5}=100^{-1}=\frac{1}{100}\)

\(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(5.20\right)^4}{\left(25.4\right)^5}=\frac{100^4}{100^5}=100^{-1}=\frac{1}{100}\)

\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4.\left(5.4\right)^4}{\left(5^2\right)^5.4^5}=\frac{5^4.5^4.4^4}{5^{10}.4^5}=\frac{5^{16}.4^4}{5^{10}.4^5}\)=\(\frac{5^6}{4}\)=\(\frac{3125}{4}\)

ủng hộ nha

\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4\left(1.15^4\right)}{\left(19^5.1\right).4^5}=\frac{5^4.15^4}{19^5.4^5}\)

\(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(5.20\right)^4}{\left(25.4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}.\)

Chúc bạn học tốt!

 = 5^4.5^4.4^4/(5^2)^5.4^5

 = 5^8.4^4/5^10.4^5

= 1/5^2.4 = 1/100

k mk nha

Ta có: \(\frac{5^4.20^4}{25^5.45}\)

=\(\frac{\left(5.20\right)^4}{\left(25.4\right)^5}\)

= \(\frac{100^4}{100^5}\)

=\(\frac{1}{100}\)

Ta có

\(E=\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\cdot\frac{5^4.20^4}{25^5.4^5}\)

\(=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\cdot\frac{2^8.5^8}{5^{10}.2^{10}}\)

\(=\frac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}\cdot\frac{1}{5^2.2^2}\)

\(=\frac{\left(-2\right)}{6}\cdot\frac{1}{100}=-\frac{1}{3}\cdot\frac{1}{100}=-\frac{1}{300}\)

Vậy : \(E=-\frac{1}{300}\)

Bài làm

\(E=\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}.\frac{5^4.20^4}{25^5.4^5}\)

\(\Rightarrow E=\frac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}.\frac{5^4.4^4.5^4}{5^{10}.4^5}\)

\(\Rightarrow E=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}.\frac{5^8.4^4}{5^{10}.4^5}\)

\(\Rightarrow E=\frac{2^{10}\left(3^8-3^9\right)}{2^{10}\left(3^8+3^8.5\right)}.\frac{1}{5^2.4}\)

\(\Rightarrow E=\frac{3^8-3^9}{3^8\left(1+5\right)}.\frac{1}{100}\)

\(\Rightarrow E=\frac{3^8\left(1-3\right)}{3^8\left(1+5\right)}.\frac{1}{100}\)

\(\Rightarrow E=-\frac{2}{6}.\frac{1}{100}\)

\(\Rightarrow E=-\frac{1}{300}\)

\(\dfrac{1}{100}\)

\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4.\left(5.2^2\right)^4}{\left(5^2\right)^5.\left(2^2\right)^5}=\frac{5^4.5^4.2^8}{5^{10}.2^{10}}=\frac{5^8.2^8}{2^{10}.2^{10}}=\frac{1}{5^2.5^2}=\frac{1}{25.4}=\frac{1}{100}\)

100000000

100000000000

=1/1000

Ê , làm thế này nhanh hơn đấy : 
 (5.20)^4/ (25.4)^5 = 100^4/100^5 = 1/100

TL:

\(5^4.20^4=100^4\)

\(25^5.4^5=100^5\)

HT

@@@@@

TL:

\(5^4.20^4=100^4\)

\(25^4.4^5=100^5\)

HT

@@@@@@@@