Question

So sánh :

a. ( 0.1)¹⁰ và ( 0.3)²⁰

b. \(\left(\dfrac{-1}{2}\right)^{5^{1^3}}\) và \(\left(\dfrac{-1}{3}\right)^{3^{1^5}}\)

Answer 1

a) \(\left(0,1\right)^{10}\) và \(\left(0,3\right)^{20}\)

Vì \(\left\{{}\begin{matrix}0,1< 0,3\\10< 20\end{matrix}\right.\)

\(\Rightarrow\left(0,3\right)^{20}>\left(0,1\right)^{10}\)

b) \(\left(-\dfrac{1}{2}\right)^{5^{1^3}}\) và \(\left(-\dfrac{1}{3}\right)^{3^{1^5}}\)

Vì \(\left\{{}\begin{matrix}\left(-\dfrac{1}{2}\right)^{5^{1^3}}=\left(-\dfrac{1}{2}\right)^5\\\left(-\dfrac{1}{3}\right)^{3^{1^5}}=\left(-\dfrac{1}{3}\right)^3\end{matrix}\right.\)

Mà \(\left\{{}\begin{matrix}-\dfrac{1}{2}< -\dfrac{1}{3}\\5>3\end{matrix}\right.\)

\(\Rightarrow\left(-\dfrac{1}{2}\right)^5< \left(-\dfrac{1}{3}\right)^3\)

Vậy

\(\left(-\dfrac{1}{2}\right)^{5^{1^3}}\) < \(\left(-\dfrac{1}{3}\right)^{3^{1^5}}\)