Question

So sánh

(1/16)¹⁰ và  (1/2)⁵⁰

(0,1)¹⁰ và (0,3)²⁰

2³⁰⁰ và 3²⁰⁰

Answer 1

Ta có: \(\left(\frac{1}{16}\right)^{10}=\left(\frac{1}{2^4}\right)^{10}=\frac{1}{2^{40}}\)

\(\left(\frac{1}{2}\right)^{50}=\frac{1}{2^{50}}\)

Vì \(2^{40}< 2^{50}\Rightarrow\frac{1}{2^{40}}>\frac{1}{2^{50}}\)hay \(\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{2}\right)^{50}\)

Answer 2

Ta có: \(\left(0,3\right)^{20}=\left[\left(0,3\right)^2\right]^{10}=\left(0,09\right)^{10}\)

Vì \(0,09< 0,1\Rightarrow\left(0,09\right)^{10}< \left(0,1\right)^{100}\)

hay \(\left(0,3\right)^{20}< \left(0,1\right)^{10}\)

Answer 3

Ta có: \(2^{300}=\left(2^3\right)^{100}=8^{100}\)

\(3^{200}=\left(3^2\right)^{100}=9^{100}\)

Vì \(8^{100}< 9^{100}\)nên \(2^{300}< 3^{200}\)

Answer 4

\(\left(\frac{1}{16}\right)^{10}=\left(\frac{1}{2}\right)^{40}\Rightarrow\left(\frac{1}{16}\right)^{10}< \left(\frac{1}{2}\right)^{50}\)

\(\left(\frac{1}{10}\right)^{10}< \left(\frac{3}{10}\right)^{20}\)

\(2^{300}=6^{100};3^{200}=6^{100}\Rightarrow2^{300}=3^{200}\)