a) \(3^2.\frac{1}{243}.81^3.\frac{1}{33}\)

\(=\frac{3^2}{243}.\frac{81^3}{33}\)

\(=\frac{3^2}{3^5}.\frac{3^{12}}{3.11}\)

\(=\frac{1}{3^3}.\frac{3^{11}}{11}\)

\(=\frac{3^8}{11}.\)

b) \(42^5:\left(2^3.\frac{1}{16}\right)\)

\(=42^5:\frac{2^3}{16}\)

\(=42^5:\frac{2^3}{2^4}\)

\(=42^5:\frac{1}{2}\)

\(=42^5.2\)

\(=21^5.2^5.2\)

\(=21^5.2^6.\)

c) \(12^5.\frac{12^2}{9^3.4^5}\)

\(=\frac{12^7}{9^3.4^5}\)

\(=\frac{3^7.4^7}{3^6.4^5}\)

\(=3.4^2\)

\(=48.\)

d) \(\frac{2^5+2^6+2^7}{2^7+2^8+2^9}\)

\(=\frac{2^5\left(1+2+2^2\right)}{2^7\left(1+2+2^2\right)}\)

\(=\frac{2^5}{2^7}\)

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

cảm ơn bn nhiều

\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{a+b-c}{b+c-d}\Rightarrow\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=\left(\frac{a+b-c}{b+c-d}\right)^3\)

Mà \(\left(\frac{a}{b}\right)^3=\frac{a}{b}\cdot\frac{a}{b}\cdot\frac{a}{b}=\frac{a}{b}\cdot\frac{b}{c}\cdot\frac{c}{d}=\frac{a}{d}\)

=>\(\left(\frac{a+b-c}{b+c-d}\right)^3=\frac{a}{d}\Rightarrow\frac{\left(a+b-c\right)^3}{\left(b+c-d\right)^3}=\frac{a}{d}\Rightarrow\frac{\left(a+b-c\right)^3}{a}=\frac{\left(b+c-d\right)^3}{d}\) (đpcm)

ta có S = 1.2.3 + 2.3.4 + ..... + 198.199.200

4s = 1.2.3.4 + 2.3.4.(5-1)+....+198.199.200.(201-197)

= 1.2.3.4+2.3.4.5-1.2.3.4+...+198.199.200.201-197.198.199.200

= 198.199.200.201

=> s = \(\frac{198.199.200.201}{4}=198.199.50.201\)

\(\frac{-5}{6}.\frac{120}{25}< x< \frac{-7}{15}.\frac{9}{14}\)

<=>  \(-4< x< -0,3\)

p/s: do k biết điều kiện của x nên mk làm đến đó

      chúc bạn học tốt

mọi người làm tỉ lệ  thức giùm mình nhé

Gọi 3 phân số đó là:  a, b, c   

Theo bài ra ta có:

\(a+b+c=\frac{-213}{70}\)

 \(a:b:c=\frac{3}{5}:\frac{4}{1}:\frac{5}{2}\)=>   \(\frac{a}{\frac{3}{5}}=\frac{b}{4}=\frac{c}{\frac{5}{2}}\)hay   \(\frac{a}{6}=\frac{b}{40}=\frac{c}{25}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{a}{6}=\frac{b}{40}=\frac{c}{25}=\frac{a+b+c}{6+40+25}=\frac{-\frac{213}{70}}{71}=-\frac{3}{70}\)

đến đây bạn tự tính nhé

\(\frac{3}{2}:\left(x-\frac{5}{3}\right)-\frac{17}{3}=\frac{11}{3}\)

<=>  \(\frac{3}{2}:\left(x-\frac{5}{3}\right)=\frac{28}{3}\)

<=>  \(x-\frac{5}{3}=\frac{9}{56}\)

<=>  \(x=1\frac{139}{168}\)

Vậy...

\(\frac{3}{2}:\left(x-\frac{5}{3}\right)-\frac{17}{3}=\frac{11}{3}\)

\(\frac{3}{2}:\left(x-\frac{5}{3}\right)=\frac{11}{3}+\frac{17}{3}\)

\(\frac{3}{2}:\left(x-\frac{5}{3}\right)=9\)

\(\left(x-\frac{5}{3}\right)=\frac{3}{2}:9\)

\(x-\frac{5}{3}=\frac{1}{6}\)

\(x=\frac{1}{6}+\frac{5}{3}=\frac{11}{6}\)

tính nhanh nhá

:(((( sao dis tau z