Question

So sánh: \(\left(\frac{1}{3}\right)^{202}\)và \(\left(\frac{1}{2}\right)^{303}\)

 

Answer 1

\(\left(\frac{1}{3}\right)^{202}=\left[\left(\frac{1}{3}\right)^2\right]^{101}=\left(\frac{1}{9}\right)^{101}=\frac{1}{9^{101}}\)

\(\left(\frac{1}{2}\right)^{303}=\left[\left(\frac{1}{2}\right)^3\right]^{101}=\left(\frac{1}{8}\right)^{101}=\frac{1}{8^{101}}\)

Ta có: \(9>8\Rightarrow9^{101}>8^{101}\Rightarrow\frac{1}{9^{101}}< \frac{1}{8^{101}}\)

\(\Rightarrow\left(\frac{1}{2}\right)^{303}>\left(\frac{1}{3}\right)^{202}\)