So sánh hai phân số: (1/243)^9 và (1/83)^13

* Hướng dẫn giải

${\left(\frac{1}{243}\right)}^9={\left(\frac{1}{3^4}\right)}^9=\frac{1}{3^{36}}$

${\left(\frac{1}{83}\right)}^{13}<{\left(\frac{1}{81}\right)}^{13}={\left(\frac{1}{3^4}\right)}^{13}=\frac{1}{3^{52}}$

Mà $\frac{1}{3^{36}}<\frac{1}{3^{42}}\Rightarrow {\left(\frac{1}{81}\right)}^{13}<{\left(\frac{1}{243}\right)}^9$

Vậy ${\left(\frac{1}{83}\right)}^{13}<{\left(\frac{1}{243}\right)}^9$