Question

so sánh 16/25^10 và 3/7^40

Answer 1

Ta có:

\(\left(\dfrac{16}{25}\right)^{10}=\left(\dfrac{4^2}{5^2}\right)^{10}=\left(\dfrac{4}{5}\right)^{2.10}=\left(\dfrac{4}{5}\right)^{20}\)

\(\left(\dfrac{3}{7}\right)^{40}=\left(\dfrac{3}{7}\right)^{2.20}=\left(\dfrac{3^2}{7^2}\right)^{20}=\left(\dfrac{9}{49}\right)^{20}\)

dễ thấy:

\(\left(\dfrac{4}{5}\right)^{20}>\left(\dfrac{9}{49}\right)^{20}\) nên \(\left(\dfrac{16}{25}\right)^{10}>\left(\dfrac{3}{7}\right)^{40}\)