Question

Các bài toán Dạng SO SÁNH SỐ HỮU TỈ:

1, \(3^{800}\)và \(5^{500}\)

2, \(\left(-2\right)^{3000}\)và \(\left(-3\right)^{2000}\)

3, \(\left(\frac{1}{2^5}\right)^{25}\)và \(\left(\frac{1}{3^{25}}\right)^5\)

4, \(6^{1000}\)và \(2^{2500}\)

 

Answer 1

3. \(\left(\frac{1}{2^5}\right)^{25}=\left(\frac{1^5}{2^5}\right)^{25}=\left[\left(\frac{1}{2}\right)^5\right]^{25}=\left(\frac{1}{2}\right)^{125}\)

\(\left(\frac{1}{3^{25}}\right)^5=\left(\frac{1^{25}}{3^{25}}\right)^5=\left[\left(\frac{1}{3}\right)^{25}\right]^5=\left(\frac{1}{3}\right)^{125}\)

Vì \(\frac{1}{2}>\frac{1}{3}\Rightarrow\left(\frac{1}{2^5}\right)^{25}>\left(\frac{1}{3^{25}}\right)^5\)

Answer 2

1. \(3^{800}=\left(3^8\right)^{100}=6561^{100}\)

\(5^{500}=\left(5^5\right)^{100}=3125^{100}\)

Vì \(6561>3125\Rightarrow3^{800}>5^{500}\)

2. \(\left(-2\right)^{3000}=\left[\left(-2\right)^3\right]^{1000}=\left(-8\right)^{1000}\)

\(\left(-3\right)^{2000}=\left[\left(-3\right)^2\right]^{1000}=9^{1000}\)

Vì \(-8< 9\Rightarrow\left(-2\right)^{3000}< \left(-3\right)^{2000}\)

Answer 3

\(6^{1000}=6^{500.2}=\left(6^2\right)^{500}=36^{500}\)

\(2^{2500}=2^{5.500}=\left(2^5\right)^{500}=32^{500}\)

\(36^{500}>32^{500}\Rightarrow6^{1000}>2^{2500}\)