Question

so sánh (-1/3)^500 với (-1/5)^300

Answer 1

Ta có:

\(\left(\dfrac{-1}{3}\right)^{500}=\left(\dfrac{1}{3}\right)^{500}=\dfrac{1}{3^{500}}=\dfrac{1}{3^{5^{100}}}=\dfrac{1}{243^{100}}\)

\(\left(\dfrac{-1}{5}\right)^{300}=\left(\dfrac{1}{5}\right)^{300}=\dfrac{1}{5^{300}}=\dfrac{1}{5^{3^{100}}}=\dfrac{1}{125^{100}}\)

Vì 243¹⁰⁰ > 125¹⁰⁰ nên \(\dfrac{1}{243^{100}}\) < \(\dfrac{1}{125^{100}}\). \(\Rightarrow\) \(\left(\dfrac{-1}{3}\right)^{500}\)< \(\left(\dfrac{-1}{5}\right)^{300}\)

Vậy...