a) \(A=\frac{2^4.25^4}{10^5.5^5}=\frac{2^4.\left(5^2\right)^4}{\left(2.5\right)^5.5^5}=\frac{2^4.5^8}{2^5.5^{10}}=\frac{1}{2.5^2}=\frac{1}{50}\)

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

\(B=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}=\frac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}=\frac{-2}{6}=\frac{-1}{3}\)

\(A=\frac{2^4.25^4}{10^5.5^5}\)

\(A=\frac{2^4.\left(5^2\right)^4}{\left(2.5\right)^5.5^5}\)

\(A=\frac{2^4.5^8}{2^5.5^5.5^5}\)

\(A=\frac{5^8}{2.5^{10}}\)

\(A=\frac{1}{2.5^2}=\frac{1}{2.25}=\frac{1}{50}\)

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

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

\(B=\frac{2^{10}.3^8-2^{10}.2.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)

\(B=\frac{2^{10}.\left(3^8-2.3^9\right)}{2^{10}.\left(3^8+3^8.5\right)}\)

\(\Rightarrow B=\frac{3^8.2.3^9}{3^8+3^8.5}\) ( \(2^{10}\ne0\))

\(B=\frac{3^8.\left(1-2.3\right)}{3^8.\left(1+5\right)}\)

\(B=\frac{1-6}{1+5}\left(3^8\ne0\right)\)

\(B=\frac{-5}{6}\)

Tham khảo nhé~

$\textbf{a)}$

$y=\dfrac{\left(\dfrac49\right)^2\cdot\left(-\dfrac9{16}\right)\cdot(-1)^{19}}{\left(\dfrac4{25}\right)^2\cdot\left(-\dfrac{25}{144}\right)^2\cdot\left(-\dfrac{49}{144}\right)^2}$

$=\dfrac{\dfrac{16}{81}\cdot\left(-\dfrac9{16}\right)\cdot(-1)}{\dfrac{16}{625}\cdot\dfrac{625}{144^2}\cdot\dfrac{49^2}{144^2}}$

$=\dfrac{\dfrac19}{\dfrac{49^2}{144^4}}$

$=\dfrac19\cdot\dfrac{144^4}{49^2}$

$=\dfrac19\cdot\dfrac{(2^4\cdot3^2)^4}{7^4}$

$=\dfrac{2^{16}\cdot3^6}{7^4}$

$=\dfrac{47775744}{2401}.$

$\textbf{b)}$

$B=\dfrac{3^8\cdot20^5}{6^8\cdot10^2}$

$=\dfrac{3^8\cdot(2^2\cdot5)^5}{(2\cdot3)^8\cdot(2\cdot5)^2}$

$=\dfrac{3^8\cdot2^{10}\cdot5^5}{2^8\cdot3^8\cdot2^2\cdot5^2}$

$=5^3$

$=125.$

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!

1/9.27ⁿn=3ⁿ

1/9=3ⁿ:27ⁿ

1/9=(1/9)ⁿ

=>n=1

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

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

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

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

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

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

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

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

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

1)  A = -1 / 3

2)  B = -35 / 2

  Chúc em làm bài tốt !

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

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

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

\(A=\frac{2^{10}.\left(3^8-3^9\right)}{2^{10}.3^8.\left(1-5\right)}=\frac{3^8-3^9}{3^8.\left(-4\right)}=\frac{3^8.\left(1-3\right)}{3^8.\left(-4\right)}=\frac{-2}{-4}=\frac{1}{2}\)

Vậy A = \(\frac{1}{2}\)

\(B=\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)

\(B=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)

\(B=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)

\(B=\frac{2^{19}.3^9+3^9.2^{18}.5}{2^{19}.3^9+2^{20}.3^{10}}\)

\(B=\frac{2^{18}.3^9.\left(2+5\right)}{2^{19}.3^9\left(1+2.3\right)}=\frac{7}{2.7}=\frac{1}{2}\)

Vậy B = \(\frac{1}{2}\)