\(-\frac{1}{27}=-\frac{1}{3^3}\) => \(\left(-\frac{1}{27}\right)^{53}=\left(\left(-\frac{1}{3}\right)^3\right)^{53}=\left(-\frac{1}{3}\right)^{159}\)

\(-\frac{1}{243}=-\frac{1}{3^5}\) => \(\left(-\frac{1}{243}\right)^{23}=\left(\left(-\frac{1}{3}\right)^5\right)^{23}=\left(-\frac{1}{3}\right)^{115}\)

vẬY \(\left(-\frac{1}{27}\right)^{53}< \left(-\frac{1}{243}\right)^{23}\)

\(\left(\frac{-1}{27}\right)^{53}\)=\(\left(\frac{-1}{3}\right)^{3X53}\)=\(\left(\frac{-1}{3}\right)^{159}\)

\(\left(\frac{-1}{243}\right)^{23}\)=\(\left(\frac{-1}{3}\right)^{5X23}\)=\(\left(\frac{-1}{3}\right)^{115}\)

=>\(\left(\frac{-1}{3}\right)^{159}\)>\(\left(\frac{-1}{3}\right)^{115}\)

=>\(\left(\frac{-1}{27}\right)^{53}\)>\(\left(\frac{-1}{243}\right)^{23}\)

a)Ta có:

 \(\left(\frac{1}{2}\right)^{27}=\left[\left(\frac{1}{2}\right)^3\right]^9=\left(\frac{1}{8}\right)^9\)

\(\left(\frac{1}{3}\right)^{18}=\left[\left(\frac{1}{3}\right)^2\right]^9=\left(\frac{1}{9}\right)^9\)

Vì \(\left(\frac{1}{8}\right)^9>\left(\frac{1}{9}\right)^9\) nên \(\left(\frac{1}{2}\right)^{27}>\left(\frac{1}{3}\right)^{18}\)

\(\left(\frac{1}{27}\right)^{23}=\frac{1^{23}}{27^{23}}=\frac{1}{\left(3^3\right)^{23}}=\frac{1}{3^{69}}\)

\(\left(\frac{1}{81}\right)^{16}=\frac{1^{16}}{81^{16}}=\frac{1}{\left(3^4\right)^{16}}=\frac{1}{3^{64}}\)

Vì 3⁶⁹ > 3⁶⁴

\(\frac{1}{3^{69}}< \frac{1}{3^{64}}\)

\(\left(\frac{1}{27}\right)^{23}=\frac{1^{23}}{27^{23}}=\frac{1}{\left(3^3\right)^{23}}=\frac{1}{3^{69}}\)

\(\left(\frac{1}{81}\right)^{16}=\frac{1^{16}}{81^{16}}=\frac{1}{\left(3^4\right)^{16}}=\frac{1}{3^{64}}\)

Vì 3⁶⁹ > 3⁶⁴

=> \(\frac{1}{3^{69}}< \frac{1}{3^{64}}\)

=> \(\left(\frac{1}{27}\right)^{23}< \left(\frac{1}{81}\right)^{16}\)

Chỉ biết \(x\) = \(\frac{109}{6075}\) thôi

 Theo  thứ tự nhé

a) <

b) <

c) >