( - 1/5 )^300 và ( - 1/5)^500

Lời giải:

\({\left( { - \frac{1}{5}} \right)^{300}}\) và \({\left( { - \frac{1}{5}} \right)^{500}}\)

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

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

Do \(\frac{1}{{125}} > \frac{1}{{243}} > 0\) nên \({\left( {\frac{1}{{125}}} \right)^{100}} > {\left( {\frac{1}{{243}}} \right)^{100}}\).

Vậy \({\left( { - \frac{1}{5}} \right)^{300}} > {\left( { - \frac{1}{5}} \right)^{500}}\).