Question

so sanh

a,\(2^{63}va3^{42}\)

b, \(5^{400}va25^{200}\)

c, \(\left(\dfrac{-1}{16}\right)^{100}va\left(\dfrac{-1}{2}\right)^{500}\)

giup minh nhe minh dang can gap

Answer 1

a, Có: \(25^{200}=\left(5^2\right)^{200}=5^{400}\)

Vì \(5^{400}=5^{400}\) mà \(25^{200}=5^{400}\Rightarrow5^{400}=25^{200}\)

c, Có:

Answer 2

a/ 2⁶³ và 3⁴²

Ta có: 2⁶³=(2³)²¹=8²¹

3⁴²=(3²)²¹=9²¹

mà 8²¹<9²¹

vậy 2⁶³<3⁴²

b/5⁴⁰⁰ và 25²⁰⁰

Ta có: 25²⁰⁰=(5²)²⁰⁰=5⁴⁰⁰

mà 5⁴⁰⁰⁼5⁴⁰⁰

vậy 5⁴⁰⁰=25²⁰⁰

c/ \(\left(\dfrac{-1}{16}\right)^{100}v\text{à}\left(\dfrac{-1}{2}\right)^{500}\)

Ta có: \(\left(\dfrac{-1}{2}\right)^{500}=\left(\left(\dfrac{-1}{2}\right)^5\right)^{100}=\left(\dfrac{-1}{32}\right)^{100}\)

mà: \(\left(\dfrac{-1}{16}\right)^{100}< \left(\dfrac{-1}{32}\right)^{100}\)

vậy\(\left(\dfrac{-1}{16}\right)^{100}< \left(\dfrac{-1}{2}\right)^{500}\)