Hình như sai đề bài bạn nhé! Đề bài đúng như dưới nhé!

\(\frac{3}{4}\).\(\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}.\frac{48}{49}\)

= \(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}.\frac{5.7}{6.6}.\frac{6.8}{7.7}\)

= \(\left(\frac{1.2.3.4.5.6}{2.3.4.5.6.7}\right).\left(\frac{3.4.5.6.7.8}{2.3.4.5.6.7}\right)\)

= \(\frac{1}{7}.\frac{8}{2}\)

= \(\frac{1}{7}.4=\frac{4}{7}\)

35/27 x 18/49 = 35x18/27x49 = 630/1323 = 10/21

18/25 x 36/125 = 18x36/25x125 = 648/3125 

mình ko bt đúng ko nữa nếu sai thì thông cảm nha

các bạn có cách nào mà làm mẫu số chung nhỏ nhất mà ko cần rút gọn được ko

\(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{50^2}{49.51}=\frac{\left(1.2.3.4...50\right)^2}{1.2.3.4...50.51}=\frac{1.2.3...50}{51}=\frac{50!}{51}\)

\(\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}\cdot\cdot\cdot\frac{50^2}{49\cdot51}\)

\(=\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}\cdot\frac{5^2}{4\cdot6}\cdot\frac{7^2}{5\cdot7}\cdot\cdot\cdot\frac{50^2}{49\cdot51}\)

\(=\frac{2}{1}\cdot\frac{50}{51}=\frac{100}{51}\)

\(\frac{12}{18}+\frac{1}{3}+\frac{1}{7}+\frac{2}{8}+\frac{27}{36}+\frac{42}{49}\)

\(=\frac{2}{3}+\frac{1}{3}+\frac{1}{7}+\frac{1}{4}+\frac{3}{4}+\frac{6}{7}\)

\(=\left(\frac{2}{3}+\frac{1}{3}\right)+\left(\frac{1}{7}+\frac{6}{7}\right)+\left(\frac{1}{4}+\frac{3}{4}\right)\)

\(=1+1+1\)

\(=3\)

Đề bài ???

 

\(\frac{2^2}{1.3}\times\frac{3^2}{2.4}\times............................\times\frac{50^2}{49.50}\)

\(=\frac{2.2}{1.3}\times\frac{3.3}{2.4}\times....................\times\frac{50.50}{49.50}\)

\(=\frac{\left(2.3.4..............50\right)\left(2.3.4............50\right)}{\left(1.2.3.............49\right)\left(3.4.5...........50\right)}\)

\(=\frac{50}{49}.2\)

\(=\frac{100}{49}\)

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

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

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

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

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

$=\dfrac19\cdot\dfrac{2^{16}\cdot3^8}{7^4}$

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

$=\dfrac{65536\cdot729}{2401}$

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