\(\left(\dfrac{1}{10}\right)^{15}=\left[\left(\dfrac{1}{10}\right)^3\right]^5=\left(\dfrac{1}{1000}\right)^5=\left(\dfrac{10}{10000}\right)^5\)
\(\left(\dfrac{3}{10}\right)^{20}=\left[\left(\dfrac{3}{10}\right)^4\right]^5=\left(\dfrac{81}{10000}\right)^5\)
\(\dfrac{10}{10000}< \dfrac{81}{10000}\)
\(\Rightarrow\left(\dfrac{10}{10000}\right)^5< \left(\dfrac{81}{10000}\right)^5\)
\(\Rightarrow\left(\dfrac{1}{10}\right)^{15}< \left(\dfrac{3}{10}\right)^{20}\)
Ta có:
\(\left(\dfrac{1}{10}\right)^{15}=\left[\left(\dfrac{1}{10}\right)^3\right]^5=\left(\dfrac{1}{1000}\right)^5\)
\(\left(\dfrac{3}{10}\right)^{20}=\left[\left(\dfrac{3}{10}\right)^4\right]^5=\left(\dfrac{81}{10000}\right)^5\)
Ta thấy: \(\dfrac{1}{1000}< \dfrac{81}{10000}\)
\(\Rightarrow\left(\dfrac{1}{1000}\right)^5< \left(\dfrac{81}{10000}\right)^5\)
\(\Rightarrow\left(\dfrac{1}{10}\right)^{15}< \left(\dfrac{3}{10}\right)^{20}\)
\(\left(\dfrac{3}{10}\right)^{20}=3^{20}.\left(\dfrac{1}{10}\right)^{20}\)
\(=3^{20}.\left(\dfrac{1}{10}\right)^5.\left(\dfrac{1}{10}\right)^{15}\)
\(=\dfrac{3^{20}}{10^5}.\left(\dfrac{1}{10}\right)^{15}\)
\(=\left(\dfrac{81}{5}\right)^5.\left(\dfrac{1}{10}\right)^{15}\)
Mà \(\left(\dfrac{1}{10}\right)^{15}=\left(\dfrac{1}{10}\right)^{15}\)
\(\Rightarrow\left(\dfrac{3}{10}\right)^{20}>\left(\dfrac{1}{10}\right)^{15}\)
\(\left(\dfrac{3}{10}\right)^{20}=3^{20}.\left(\dfrac{1}{10}\right)^{20}=\left(\dfrac{81}{5}\right)^5.\left(\dfrac{1}{10}\right)^{15}\)
\(\Rightarrow\left(\dfrac{1}{10}\right)^{15}< \left(\dfrac{81}{5}\right)^5.\left(\dfrac{1}{10}\right)^{15}\)
\(\Rightarrow\left(\dfrac{1}{10}\right)^{15}< \left(\dfrac{3}{10}\right)^{20}\)
