So sánh:
\(\left(\dfrac{1}{2}\right)^{3000}=\left[\left(\dfrac{1}{2}\right)^3\right]^{1000}=\left(\dfrac{1}{8}\right)^{1000}\)
\(\left(\dfrac{1}{3}\right)^{2000}=\left[\left(\dfrac{1}{3}\right)2\right]^{1000}=\left(\dfrac{1}{9}\right)^{1000}\)
Vì \(\dfrac{1}{8}>\dfrac{1}{9}\)
Nên \(\left(\dfrac{1}{8}\right)^{1000}>\left(\dfrac{1}{9}\right)^{1000}\)
Vậy \(\left(\dfrac{1}{2}\right)^{3000}>\left(\dfrac{1}{3}\right)^{2000}\)