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

Đề bài là gì vậy ( rút gọn hả?)

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{25^2\left(5.4\right)^4}{25^5.4^5}=\dfrac{1.5^4.4^4}{25^3.4^5}=\dfrac{25^2.1}{25^3.4}=\dfrac{1}{25.4}=\dfrac{1}{100}\)

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.\left(5.4\right)^4}{\left(5^2\right)^5.4^5}=\dfrac{5^4.5^4.4^4}{5^{10}.4^5}=\dfrac{5^8.4^8}{5^{10}.4^5}=\dfrac{1.1}{5^2.4}=\dfrac{1}{100}\)

Ta có:

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.5^4.4^4}{\left(5^2\right)^5.4^5}=\dfrac{5^8.4^4}{5^{10}.4^5}=\dfrac{1}{5^2.4}=\dfrac{1}{25.4}=\dfrac{1}{100}=0,01\)

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.\left(4.5\right)^4}{\left(5.5\right)^5.4^5}=\dfrac{5^4.4^4.5^4}{5^5.5^5.4^5}=\dfrac{1}{5.5.4}=\dfrac{1}{100}\)

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.\left(5.4\right)^4}{\left(5^2\right)^5.4^5}=\dfrac{5^4.5^4.4^4}{5^{10}.4^5}=\dfrac{5^8.4^4}{5^8.5^2.4.4^4}=\dfrac{1}{100}\)

\(\dfrac{5^4\cdot20^4}{25^5\cdot4^5}=\dfrac{\left(5\cdot20\right)^4}{\left(25\cdot4\right)^5}=\dfrac{100^4}{100^5}=\dfrac{1}{100}\)

\(\dfrac{4^5\cdot9^4}{8^3\cdot27^3}=\dfrac{\left(2^2\right)^5\cdot\left(3^2\right)^4}{\left(2^3\right)^3\cdot\left(3^3\right)^3}=\dfrac{2^{10}\cdot3^8}{2^9\cdot3^9}=\dfrac{2}{3}\)

\(\dfrac{4^{20}\cdot3^{35}}{2^{37}\cdot27^{12}}=\dfrac{\left(2^2\right)^{20}\cdot3^{35}}{2^{37}\cdot\left(3^3\right)^{12}}=\dfrac{2^{40}\cdot3^{35}}{2^{37}\cdot3^{36}}=\dfrac{2^3}{3}\)

\(\dfrac{5^4\cdot20^4}{25^5\cdot4^5}=\dfrac{5^4\cdot5^4\cdot4^4}{5^5\cdot5^5\cdot4^5}=\dfrac{1}{5^2\cdot4}=\dfrac{1}{100}\)

\(\dfrac{2^{15}\cdot9^4}{6^6\cdot8^3}=\dfrac{2^{15}\cdot\left(3^2\right)^4}{2^6\cdot3^6\cdot\left(2^3\right)^3}=\dfrac{2^{15}\cdot3^8}{2^6\cdot3^6\cdot2^9}=3^2\)

\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4.\left(4.5\right)^4}{\left(5.5\right)^5.4^5}=\frac{5^4.4^4.5^4}{5^5.5^5.4^5}=\frac{5^8.4^4}{5^8.5^2.4^4.4}=\frac{1}{5^2.4}=\frac{1}{100}\)

\(\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.\left(4.5\right)^4}{25^5.4^5}=\dfrac{5^4.4^4.5^4}{25^5.4^5}=\dfrac{\left(5^4.5^4\right).4^4}{25^5.4^5}=\dfrac{25^4.4^4}{25^5.4^5}=\dfrac{1.1}{25.4}=\dfrac{1}{100}\)

a: \(=\dfrac{5^4\cdot5^4\cdot2^8}{5^{10}\cdot2^{10}}=\dfrac{1}{5^2}\cdot\dfrac{1}{2^2}=\dfrac{1}{100}\)

b: \(=\left(\dfrac{12+8-3}{12}\right)\cdot\left(\dfrac{16-15}{20}\right)^2\)

\(=\dfrac{17}{12}\cdot\dfrac{1}{400}=\dfrac{17}{4800}\)