a) \(\left(\frac{1}{80}\right)^7>\left(\frac{1}{81}\right)^7=\left(\frac{1}{3^4}\right)^7=\frac{1}{3^{4.7}}=\frac{1}{3^{28}}\)
\(\left(\frac{1}{243}\right)^6=\left(\frac{1}{3^5}\right)^6=\frac{1}{3^{3.6}}=\frac{1}{3^{30}}\)
Vì \(\frac{1}{3^{28}}< \frac{1}{3^{30}}\left(3^{28}< 3^{30}\right)\)
Nên \(\left(\frac{1}{80}\right)^7< \left(\frac{1}{243}\right)^6\)
b) \(\left(\frac{3}{8}\right)^5=\frac{3^5}{\left(2^3\right)^5}=\frac{243}{2^{3.5}}=\frac{243}{2^{15}}>\frac{243}{3^{15}}>\frac{125}{3^{15}}\)
\(=\frac{5^3}{\left(3^5\right)^3}=\frac{5^3}{3^{5.3}}=\frac{5^3}{3^{15}}=\left(\frac{5}{243}\right)^3\)
\(\Rightarrow\left(\frac{3}{8}\right)^5>\left(\frac{5}{243}\right)^3\)
