\(\frac{6^8\cdot16^5}{2^{27}\cdot27^3}=\frac{\left(2\cdot3\right)^8\cdot\left(2^4\right)^5}{2^{27}\cdot\left(3^3\right)^3}\)

\(=\frac{2^8\cdot3^8\cdot2^{20}}{2^{27}\cdot3^3}=\frac{2^{28}\cdot3^8}{2^{27}\cdot3^9}=\frac{2}{3}\)

Mọi người đánh giúp mình nhé! Hạn là tối nay!!

\(\left|x+\frac{1}{3}\right|+\frac{4}{5}=\left|-3,2+\frac{2}{5}\right|+\left(27-\frac{3}{5}\right)\left(27-\frac{3^2}{6}\right)...\left(27-\frac{3^5}{9}\right)...\left(27-\frac{3^{2010}}{2014}\right)\)

\(\Leftrightarrow\left|x+\frac{1}{3}\right|+\frac{4}{5}=\frac{14}{5}+\left(27-\frac{3^2}{6}\right)\left(27-\frac{3^3}{7}\right)...\left(27-27\right)...\left(27-\frac{3^{2010}}{2014}\right)\)

\(\Leftrightarrow\left|x+\frac{1}{3}\right|+\frac{4}{5}=\frac{14}{5}\)

\(\Leftrightarrow\left|x+\frac{1}{3}\right|=2\)

\(\Rightarrow\hept{\begin{cases}x+\frac{1}{3}=2\\x+\frac{1}{3}=-2\end{cases}\Rightarrow\hept{\begin{cases}x=\frac{5}{3}\\x=-\frac{7}{3}\end{cases}}}\)

bạn ơi, có một chỗ chưa chuẩn .bạn kiểm tra lại giú mình. chỗ vế trái bạn thiếu \(\left(27-\frac{3}{5}\right)\). bạn bổ sung vào cho đúng nhé. dù sao vẫn cảm ơn bạn.

\(B=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)

\(\Rightarrow\frac{1}{3}B=\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^8}\)

\(\Rightarrow B-\frac{1}{3}B=\frac{1}{3}-\frac{1}{3^8}\Rightarrow\frac{2}{3}B=\frac{3^7-1}{3^8}\Rightarrow B=\frac{3\left(3^7-1\right)}{2.3^8}\)

Ta có : 

\(B=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{2187}\)

\(B=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)

\(3B=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\)

\(3B-B=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^6}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\right)\)

\(2B=1-\frac{1}{3^7}\)

\(2B=\frac{3^7-1}{3^7}\)

\(B=\frac{3^7-1}{3^7}:2\)

\(B=\frac{3^7-1}{2.3^7}\)

Vậy \(B=\frac{3^7-1}{2.3^7}\)

Chúc bạn học tốt ~

Bài 6: Tính nhanh

(-2)+7+(-12)+17+(-22)+27

Giải:Ta có:

 (-2)+7+(-12)+17+(-22)+27

=(7-2) + (17 - 12) + (27 - 22 )

=5 + 5 +5

=5 x 3 = 15

Vậy giá trị của ............

\(=5+5+5=15\)

\(\frac{\left(\frac{5}{8}+\frac{5}{27}-\frac{5}{49}\right)\cdot8\cdot27\cdot49}{\left(\frac{11}{8}+\frac{11}{27}-\frac{11}{49}\right)\cdot8\cdot27\cdot49}+\frac{6}{11}\)

\(=\frac{8+27-49}{8+27-49}+\frac{6}{11}\)

\(=1+\frac{6}{11}\)

\(=\frac{11}{11}+\frac{6}{11}=\frac{17}{11}\)

\(\frac{\frac{5}{8}+\frac{5}{27}-\frac{5}{49}}{\frac{11}{8}+\frac{11}{27}-\frac{11}{49}}+\frac{6}{11}\)

\(=\frac{5\left(\frac{1}{8}+\frac{1}{27}-\frac{1}{49}\right)}{11\left(\frac{1}{8}+\frac{1}{27}-\frac{1}{49}\right)}+\frac{6}{11}\)

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

(7x6=5+2+6x7) =

\(\frac{27^3.4^5}{6^8}:\left(\frac{5^5.2^4}{10^4}:\frac{6^4}{2^6.3^4}\right)\)

\(=\frac{3^9.2^{10}}{6^8}:\left(5:\frac{1}{2^2}\right)\)\(=3.2^2:20=\frac{12}{20}=\frac{3}{5}\)

\(\frac{27^3.4^5}{6^8}:\left(\frac{5^5.2^4}{10^4}:\frac{6^4}{2^6.3^4}\right)\)

\(=\frac{\left(3^3\right)^3.\left(2^2\right)^5}{\left(3.2\right)^8}:\left(\frac{5^5.2^4}{\left(5.2\right)^4}:\frac{\left(2.3\right)^4}{2^6.3^4}\right)\)

\(=\frac{3^9.2^{10}}{3^8.2^8}:\left(\frac{5^5.2^4}{5^4.2^4}:\frac{2^4.3^4}{2^6.3^4}\right)\)

\(=3.2^2:\left(5:\frac{1}{2^2}\right)\)

\(=3.4:\left(5.4\right)\)

\(=12:20\)

\(=\frac{12}{20}=\frac{3}{5}\)

a: ~12.58

b: 10

c:-1

d:55/4

dkr68