Ta có
$\left( -\dfrac{1}{5} \right)^{300} = \left[(-1)\dfrac{1}{5} \right]^{300}$
$= (-1)^{300} \left( \dfrac{1}{5} \right)^{300}$
Do 300 là số chẵn nên $(-1)^{300} = 1$. Do đó
$\left( -\dfrac{1}{5} \right)^{300} = \left( \dfrac{1}{5} \right)^{300}$
Làm tương tự ta cx có
$\left( -\dfrac{1}{3} \right)^{500} = \left( \dfrac{1}{3} \right)^{500}$
Mặt khác, ta lại có
$\left( \dfrac{1}{5} \right)^{300} = \left( \dfrac{1}{5} \right)^{3.100}$
$= \left( \dfrac{1}{5^3} \right)^{100}$
$= \left( \dfrac{1}{125} \right)^{100}$
và
$\left( \dfrac{1}{3} \right)^{500} = \left( \dfrac{1}{3} \right)^{5.100}$
$= \left( \dfrac{1}{3^5} \right)^{100}$
$= \left( \dfrac{1}{243} \right)^{100}$
Ta có
$\dfrac{1}{243} < \dfrac{1}{125}$
Do đó
$\left( \dfrac{1}{243} \right)^{100} < \left( \dfrac{1}{125} \right)^{100}$
Suy ra
$\left( \dfrac{1}{3} \right)^{500} < \left( \dfrac{1}{5} \right)^{300}$
Do đó
$\left( -\dfrac{1}{3} \right)^{500} < \left( -\dfrac{1}{5} \right)^{300}$.
