Question

\(\left(\dfrac{-1}{2}\right)^{300}\)và\(\left(\dfrac{-1}{5}\right)^{200}\) so sánh

Answer 1

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 \(\left(\dfrac{-1}{2}\right)^{300}>\left(\dfrac{-1}{5}\right)^{200}\)

Answer 2

(-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