Question

-(\(\dfrac{-1}{6}\))\(^{100}\) và -(\(\dfrac{-1}{8}\))\(^{150}\)

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Answer 1

Ta có:

\(-\left(-\dfrac{1}{6}\right)^{100}=-\left(\dfrac{1}{6}\right)^{100}=-\left[\left(\dfrac{1}{6}\right)^2\right]^{50}=-\left(\dfrac{1}{36}\right)^{50}\)

\(-\left(-\dfrac{1}{8}\right)^{150}=-\left(\dfrac{1}{8}\right)^{150}=-\left[\left(\dfrac{1}{8}\right)^3\right]^{50}=-\left(\dfrac{1}{512}\right)^{50}\)

Mà: \(\dfrac{1}{36}>\dfrac{1}{512}\)

\(\Rightarrow\left(\dfrac{1}{36}\right)^{50}>\left(\dfrac{1}{512}\right)^{50}\)

\(\Rightarrow-\left(\dfrac{1}{36}\right)^{50}< -\left(\dfrac{1}{512}\right)^{50}\)

\(\Rightarrow-\left(\dfrac{-1}{6}\right)^{100}< -\left(\dfrac{-1}{8}\right)^{150}\)