Question

So sánh

\(\left(\dfrac{1}{3}\right)^{500};\left(\dfrac{1}{5}\right)^{300}\)

Answer 1

Ta có:

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

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

Vì 243 > 125 nên \(243^{100}>125^{100}\), do đó \(\dfrac{1}{243^{100}}< \dfrac{1}{125^{100}}\)

Vậy \(\left(\dfrac{1}{3}\right)^{500}< \left(\dfrac{1}{5}\right)^{300}\)