Question

\(2^{-5n}\) và \(5^{-2n}\). So sánh hai số sau

Answer 1

\(2^{-5n}=\dfrac{1}{2^{5n}}=\dfrac{1}{32^n}\)

\(5^{-2n}=\dfrac{1}{5^{2n}}=\dfrac{1}{25^n}\)

Vì \(\dfrac{1}{32^n}< \dfrac{1}{25^n}\Rightarrow2^{-5n}< 5^{-2n}\)

Vậy...

Answer 2

Ta có : $2^{-5n}=\dfrac{1}{2^{5n}}$

$5^{-2n}=\dfrac{1}{5^{2n}}$

Lúc này ta chỉ cần so sánh $2^{5n}$ và $5^{2n}$

$2^{5n}=(2^5)^n=32^n$

$5^{2n}=(5^2)^n=25^n$

Vì $32^n>25^n$

$=>2^{5n}>5^{2n}$

$=>\dfrac{1}{2^{5n}}>\dfrac{1}{5^{2n}}$

$=>2^{-5n}<5^{-2n}$ (đổi dấu)

Answer 3

\(2^{-5n}=\dfrac{1}{2^{5n}}=\dfrac{1}{32^n}\)

\(5^{-2n}=\dfrac{1}{5^{2n}}=\dfrac{1}{25^n}\)

\(\dfrac{1}{32^n}< \dfrac{1}{25^n}\Leftrightarrow2^{-5n}< 5^{-2n}\)