Question

1) Hãy so sánh \(\left(\dfrac{1}{2}\right)^{300}\)và\(\left(\dfrac{1}{3}\right)^{200}\)

Answer 1

Ta có : \(\left(\dfrac{1}{2}\right)^{300}\) = \(\left(\left(\dfrac{1}{2}\right)^3\right)^{100}\)

\(\left(\dfrac{1}{3}\right)^{200}=\left(\left(\dfrac{1}{3}\right)^2\right)^{100}\)

Ta có : \(\left(\dfrac{1}{2}\right)^3=\dfrac{1^3}{2^3}=\dfrac{1}{2^3}=\dfrac{1}{8}\)

\(\left(\dfrac{1}{3}\right)^2=\left(\dfrac{1^2}{3^2}\right)=\dfrac{1}{3^2}=\dfrac{1}{9}\)

Vì \(\dfrac{1}{8}>\dfrac{1}{9}=>\left(\dfrac{1}{2}\right)^3>\left(\dfrac{1}{3}\right)^2\)

Vậy \(\left(\dfrac{1}{2}\right)^{300}>\left(\dfrac{1}{3}\right)^{200}\)