Question

[Yaya Nguyễn]

SO SÁNH:

a,\(\left(\frac{-1}{5}\right)^{300}\)và\(\left(\frac{-1}{3}\right)^{500}\)

b,\(50^{20}\)và\(2550^{10}\)

c,\(2^{100}\);\(3^{75}\);\(5^{50}\)

Answer 1

[Arima Kousei]

Bạn tham khảo nhé 

a )  Ta có : 

\(\left(-\frac{1}{5}\right)^{300}=\left(\frac{1}{5}\right)^{300}=\frac{1}{5^{300}}=\frac{1}{\left(5^3\right)^{100}}=\frac{1}{125^{100}}\)

\(\left(-\frac{1}{3}\right)^{500}=\left(\frac{1}{3}\right)^{500}=\frac{1}{3^{500}}=\frac{1}{\left(3^5\right)^{100}}=\frac{1}{243^{100}}\)

Do \(\frac{1}{125^{100}}>\frac{1}{243^{100}}\left(125^{100}< 243^{100}\right)\)

\(\Rightarrow\left(-\frac{1}{5}\right)^{300}>\left(-\frac{1}{3}\right)^{500}\)

b ) 

Ta có : 

\(2550^{10}=\left(50.51\right)^{10}=50^{10}.51^{10}\)

\(50^{20}=50^{10}.50^{10}\)

Do \(50^{10}.51^{10}>50^{10}.50^{10}\)

\(\Rightarrow50^{20}< 2550^{10}\)

c ) 

Ta có : 

\(2^{100}=\left(2^4\right)^{25}=16^{25}\)

\(3^{75}=\left(3^3\right)^{25}=27^{25}\)

\(5^{50}=\left(5^2\right)^{25}=25^{25}\)

Do \(16^{25}< 25^{25}< 27^{25}\)

\(\Rightarrow2^{100}< 5^{50}< 3^{75}\)

Answer 2

[Thành Vinh Lê]

b)2550¹⁰>2500¹⁰=50²⁰

=>2550¹⁰>50²⁰