Question

So sánh

\(\left(\frac{-1}{8}\right)^{100}\)và  \(\left(\frac{-1}{4}\right)^{200}\)

Answer 1

Ta có:

\(\left(\frac{-1}{8}\right)^{100}=\frac{\left(-1\right)^{100}}{8^{100}}=\frac{1}{\left(2^3\right)^{100}}=\frac{1}{2^{300}}\)

\(\left(\frac{-1}{4}\right)^{200}=\frac{\left(-1\right)^{200}}{4^{200}}=\frac{1}{\left(2^2\right)^{100}}=\frac{1}{2^{200}}\)

Vì \(2^{300}>2^{200}\)\(\Rightarrow\frac{1}{2^{300}}< \frac{1}{2^{200}}\)

\(\Rightarrow\left(\frac{-1}{8}\right)^{^{100}}< \left(\frac{-1}{4}\right)^{200}\)