a) 80<243 nên \(\frac{1}{80}>\frac{1}{243}\)

\(\Rightarrow\left(\frac{1}{80}\right)^7>\left(\frac{1}{243}\right)^7\) mà \(\left(\frac{1}{243}\right)^7>\left(\frac{1}{243}\right)^6\)

Nên \(\left(\frac{1}{80}\right)^7>\left(\frac{1}{243}\right)^6\)

b) Ta so sánh \(\frac{3}{8}\) với \(\frac{5}{243}\)

Ta có: \(\frac{3}{8}=\frac{3.243}{8.243}=\frac{729}{1944}\)

\(\frac{5}{243}=\frac{5.8}{243.8}=\frac{40}{1944}\)

Suy ra: \(\frac{3}{8}>\frac{5}{243}\)

\(\Rightarrow\left(\frac{3}{8}\right)^5>\left(\frac{5}{243}\right)^5\) mà \(\left(\frac{5}{243}\right)^5>\left(\frac{5}{243}\right)^3\)

Nên \(\left(\frac{3}{8}\right)^5>\left(\frac{5}{243}\right)^3\)

\(a,\left(\frac{1}{8}\right)^7>\left(\frac{1}{81}\right)^7=\left(\frac{1}{3^4}\right)^7=\frac{1}{3^{28}}\)

\(\left(\frac{1}{234}\right)^6=\left(\frac{1}{3^5}\right)^6=\frac{1}{3^{30}}\)

Vì \(\frac{1}{3^{28}}>\frac{1}{3^{30}}\)nên \(\left(\frac{1}{80}\right)^7>\left(\frac{1}{243}\right)^8\)

\(b,\left(\frac{3}{5}\right)^5=\left(\frac{3}{2^3}\right)^5=\frac{243}{2^{15}};\)

\(\left(\frac{5}{243}\right)^3=\left(\frac{5}{3^5}\right)^3=\frac{125}{3^{15}}\)

Chọn phân số \(\frac{243}{3^{15}}\)làm phân số trung gian để so sánh hai phân số trên , ta thấy :

\(\frac{243}{2^{15}}>\frac{243}{3^{15}}>\frac{125}{3^{15}}\)

=> \(\frac{243}{2^{15}}>\frac{125}{3^{15}}\)

Từ đó => \(\left(\frac{3}{8}\right)^5>\left(\frac{5}{243}\right)^3\)

 Theo  thứ tự nhé

a) <

b) <

c) >

\(\left(\frac{1}{80}\right)^7>\left(\frac{1}{81}\right)^7=\left(\frac{1}{3^4}\right)^7=\frac{1^7}{\left(3^4\right)^7}=\frac{1}{3^{28}}\)

\(\left(\frac{1}{243}\right)^6=\left(\frac{1}{3^5}\right)^6=\frac{1^6}{\left(3^5\right)^6}=\frac{1}{3^{30}}\)

Vì \(\frac{1}{3^{28}}>\frac{1}{3^{30}}\) nên \(\left(\frac{1}{80}\right)^7>\left(\frac{1}{243}\right)^6\)