Ta có:\(\left(\dfrac{-1}{2}\right)^{300}=\left[\left(\dfrac{-1}{2}\right)^3\right]^{100}=\left(\dfrac{-1}{8}\right)^{100}=\left(\dfrac{1}{8}\right)^{100}\)
\(\left(\dfrac{-1}{5}\right)^{200}=\left[\left(\dfrac{-1}{5}\right)^2\right]^{100}=\left(\dfrac{-1}{25}\right)^{100}=\left(\dfrac{1}{25}\right)^{100}\)
Vì \(\dfrac{1}{8}>\dfrac{1}{25}\) nên \(\left(\dfrac{1}{8}\right)^{100}>\left(\dfrac{1}{25}\right)^{100}\)
Vậy \(\left(\dfrac{-1}{2}\right)^{300}>\left(\dfrac{-1}{5}\right)^{200}\)
(-1/2)³⁰⁰ = [(-1/2)³]¹⁰⁰ = (-1/8)¹⁰⁰ = (1/8)¹⁰⁰
(-1/5)²⁰⁰ = [(-1/5)²]¹⁰⁰ = (1/25)¹⁰⁰
Do 8 < 25 nên 1/8 > 1/25
Suy ra (1/8)¹⁰⁰ > (1/25)¹⁰⁰
Vậy (-1/2)³⁰⁰ > (-1/5)²⁰⁰
