\(\frac{6^8.16^5}{2^{27}.27^3}\)

\(=\frac{\left(2.3\right)^8.\left(2^4\right)^5}{2^{27}.\left(3^3\right)^3}\)

\(=\frac{2^8.3^8.2^{20}}{2^{27}.3^9}\)

\(=\frac{2^{28}.3^8}{2^{27}.3^9}\)

\(=\frac{2}{3}\)

Ta có: \(\frac{6^8.16^5}{2^{27}.27^3}\)

=\(\frac{\left(2.3\right)^8.\left(2^4\right)^5}{2^{27}.\left(3^3\right)^3}\)

=\(\frac{2^8.3^8.2^{20}}{2^{27}.3^9}\)

=\(\frac{2^{27}.2.3^8}{2^{27}.3^8.3}\)

=\(\frac{2}{3}\)

Hok tốt

a: ~12.58

b: 10

c:-1

d:55/4

dkr68

a)~12.58

b)10

c)-1

d)55/4

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

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

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

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

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

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.

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

2.\(3\sqrt{3}\)-\(6.\frac{2\sqrt{3}}{3}\)+ \(\frac{3}{5}5\sqrt{3}\)= \(6\sqrt{3}\)- \(4\sqrt{3}\)+3\(\sqrt{3}\)= \(5\sqrt{3}\)

a) \(\frac{6^{10}.27^5}{4^5.81^6}=\frac{\left(2.3\right)^{10}.\left(3^3\right)^5}{\left(2^2\right)^5.\left(3^4\right)^6}=\frac{2^{10}.3^{10}.3^{15}}{2^{10}.3^{24}}=\frac{2^{10}.3^{25}}{2^{10}.3^{24}}=\frac{3^{25}}{3^{24}}=3\)
b) \(\frac{72^3.54^2}{108^4}=\frac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}=\frac{2^9.3^6.2^2.3^6}{2^8.3^{12}}=\frac{2^{11}.3^{12}}{2^8.3^{12}}=\frac{2^{11}}{2^8}=2^3=8\)
c) \(\frac{27^4.2^3-3^{10}.4^3}{6^4.9^3.4}=\frac{\left(3^3\right)^4.2^3-3^{10}.\left(2^2\right)^3}{\left(2.3\right)^4.\left(3^2\right)^3.2^2}=\frac{3^{12}.2^3-3^{10}.2^6}{2^4.3^4.3^6.2^2}\)
= \(\frac{3^{12}.2^3-3^{10}.2^6}{2^6.3^{10}}=\frac{3^{12}.2^3}{2^6.3^{10}}-\frac{3^{10}.2^6}{2^6.3^{10}}=\frac{3^2}{2^3}-1=\frac{9}{8}-1=\frac{1}{8}\)