Bài giải:

Ta có: ${{\left( -\frac{1}{5} \right)}^{300}}={{\left( \frac{1}{5} \right)}^{300}}={{\left[ {{\left( \frac{1}{5} \right)}^{3}} \right]}^{100}}={{\left( \frac{1}{125} \right)}^{100}}=\frac{1}{{{125}^{100}}}$

Và ${{\left( -\frac{1}{3} \right)}^{500}}={{\left( \frac{1}{3} \right)}^{500}}={{\left[ {{\left( \frac{1}{3} \right)}^{5}} \right]}^{100}}={{\left( \frac{1}{243} \right)}^{100}}=\frac{1}{{{243}^{100}}}$

Mà $\frac{1}{{{125}^{100}}}>\frac{1}{{{243}^{100}}}\Rightarrow {{\left( -\frac{1}{5} \right)}^{300}}>{{\left( -\frac{1}{3} \right)}^{500}}$

Trả lời: >