Ta có:
\(\left(-\frac{1}{5}\right)^{300}=\left[\left(-\frac{1}{5}\right)^3\right]^{100}=\left(-\frac{1}{125}\right)^{100}=\left(\frac{1}{125}\right)^{100}.\)
\(\left(-\frac{1}{3}\right)^{500}=\left[\left(-\frac{1}{3}\right)^5\right]^{100}=\left(-\frac{1}{243}\right)^{100}=\left(\frac{1}{243}\right)^{100}.\)
Vì \(125< 243\) nên \(\frac{1}{125}>\frac{1}{243}.\)
\(\Rightarrow\left(\frac{1}{125}\right)^{100}>\left(\frac{1}{243}\right)^{100}\)
\(\Rightarrow\left(-\frac{1}{5}\right)^{300}>\left(-\frac{1}{3}\right)^{500}.\)
Chúc bạn học tốt!