`#3107.101107`

\(\dfrac{27^2\cdot2^3\cdot5^4}{15^2\cdot6^9}\)

\(=\dfrac{\left(3^3\right)^2\cdot2^3\cdot5^4}{3^2\cdot5^2\cdot2^9\cdot3^9}\)

\(=\dfrac{3^6\cdot2^3\cdot5^4}{3^{11}\cdot5^2\cdot2^9}\)

\(=\dfrac{5^2}{3^5\cdot2^6}\)

\(=\dfrac{25}{15552}\)

Đây nha:

\(\left(x-\dfrac{1}{8}\right)^3=-\dfrac{8}{125}\)

\(\left(x-\dfrac{1}{8}\right)^3=\left(\dfrac{-2}{5}\right)^3\)

\(\Rightarrow x-\dfrac{1}{8}=\dfrac{-2}{5}\)

\(x=\dfrac{-2}{5}+\dfrac{1}{8}=\dfrac{-16}{40}+\dfrac{5}{40}\)

\(x=\dfrac{-11}{40}\)

\(#WendyDang\)

\(\left(x-\dfrac{1}{3}\right)^3=\dfrac{-8}{125}\)

\(\left(x-\dfrac{1}{3}\right)^3=\left(\dfrac{-2}{5}\right)^3\)

\(\Rightarrow x-\dfrac{1}{3}=\dfrac{-2}{5}\)

\(x=\dfrac{-2}{5}+\dfrac{1}{3}=\dfrac{-6}{15}+\dfrac{5}{15}\)

\(x=\dfrac{-1}{15}\)

\(\dfrac{2^7\cdot9^3}{6^5\cdot8^2}\\ =\dfrac{2^7\cdot\left(3^2\right)^3}{\left(2\cdot3\right)^5\cdot\left(2^3\right)^2}\\ =\dfrac{2^7\cdot3^6}{2^5\cdot3^5\cdot2^6}\\ =\dfrac{2^2\cdot3}{2^6}\\ =\dfrac{4\cdot3}{64}\\ =\dfrac{12}{64}\\ =\dfrac{3}{16}\)

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

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

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

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

cảm ơn

nha❤

A = 0,(36) - 0,(71)

= 36/99 - 71/99

= -35/99

B = [3,(12) - 2,(5)] : 0,(14)

= (103/33 - 203/99) : 14/99

= 106/99 : 14/99

= 53/7

\(A=0,\left(36\right)-0,\left(71\right)\)

\(A=\dfrac{36}{99}-\dfrac{71}{99}=-\dfrac{35}{99}=-0,\left(35\right)\)

\(B=\left[3,\left(12\right)-2,\left(5\right)\right]:0,\left(14\right)\)

\(B=\left(\dfrac{3\cdot99+12}{99}-\dfrac{2\cdot9+5}{9}\right):\dfrac{14}{99}\)

\(B=\left(\dfrac{309}{99}-\dfrac{23}{9}\right):\dfrac{14}{99}\)

\(B=\dfrac{56}{99}:\dfrac{14}{99}\)

\(B=4\)

\(\dfrac{79}{11}=7+\dfrac{2}{11}=7+\dfrac{18}{99}\)

\(=7,\left(18\right)\)

\(\dfrac{91}{37}=2+\dfrac{17}{37}=2+\dfrac{459}{999}\)

\(=2,\left(459\right)\)

79/11 = 7,(18)

91/37 = 2,(459)

Chuyển đổi cụ thể:

\(\dfrac{79}{11}=\dfrac{79\cdot9}{11\cdot9}=\dfrac{711}{99}=7\dfrac{18}{99}\)

\(=7,\left(18\right)\)

\(\dfrac{79}{11}=7,\left(18\right)\)

\(\dfrac{1}{6}=0,1\left(6\right)\)

\(\dfrac{1}{3}=0,\left(3\right)\)

\(\dfrac{2}{3}=0,\left(6\right)\)

1/6 = 0,1(6)

1/3 = 0,(3)

2/3 = 0,(6)

a)\(\dfrac{27^4.4^3}{9^5.8^2}\)

=\(\dfrac{3^{12}.2^6}{3^{10}.2^6}\)

=3\(^2\)=9

b)\(\dfrac{3^{29}.4^{16}}{27^9.8^{11}}\)

=\(\dfrac{3^{29}.2^{32}}{3^{27}.2^{33}}\)

=\(\dfrac{9}{2}\)

\(\dfrac{27^4.4^3}{9^5.8^2}=\dfrac{\left(3^3\right)^4.\left(2^2\right)^3}{\left(3^2\right)^5.\left(2^3\right)^2}=\dfrac{3^{12}.2^6}{3^{10}.2^6}=\dfrac{3^{12}}{3^{10}}=3^2=9\)

_________

\(\dfrac{3^{29}.4^{16}}{27^9.8^{11}}=\dfrac{3^{29}.\left(2^2\right)^{16}}{\left(3^3\right)^9.\left(2^3\right)^{11}}=\dfrac{3^{29}.2^{32}}{3^{27}.2^{33}}=\dfrac{1}{3^2.2}=\dfrac{1}{9.2}=\dfrac{1}{18}\)