Ta có: \(\left(\dfrac{1}{16}\right)^{200}=\left(\dfrac{1}{2^4}\right)^{200}=\left(\dfrac{1}{2}\right)^{800}\)
Vì \(800< 1000\) nên \(\left(\dfrac{1}{2}\right)^{800}< \left(\dfrac{1}{2}\right)^{1000}\)
hay \(\left(\dfrac{1}{16}\right)^{200}< \left(\dfrac{1}{2}\right)^{1000}\)
\(\left(\dfrac{1}{16}\right)^{200}=\left[\left(\dfrac{1}{2}\right)^4\right]^{200}=\left(\dfrac{1}{2}\right)^{800}\)
mà \(800< 1000\) và \(0< \dfrac{1}{2}< 1\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{800}>\left(\dfrac{1}{2}\right)^{1000}\)
\(\Rightarrow\left(\dfrac{1}{16}\right)^{200}>\left(\dfrac{1}{2}\right)^{1000}\)
