7: \(\left(\dfrac{1}{2}\right)^{24}=\left(\dfrac{1}{2}\right)^{2\cdot12}=\left(\dfrac{1}{4}\right)^{12}\)
\(\left(\dfrac{1}{3}\right)^{36}=\left(\dfrac{1}{3}\right)^{3\cdot12}=\left(\dfrac{1}{27}\right)^{12}\)
mà \(\dfrac{1}{4}>\dfrac{1}{27}\)
nên \(\left(\dfrac{1}{2}\right)^{24}>\left(\dfrac{1}{3}\right)^{36}\)
8: \(\left(\dfrac{1}{5}\right)^{50}=\left[\left(\dfrac{1}{5}\right)^2\right]^{25}=\left(\dfrac{1}{25}\right)^{25}\)
\(\left(\dfrac{1}{3}\right)^{75}=\left(\dfrac{1}{3}\right)^{3\cdot25}=\left(\dfrac{1}{27}\right)^{25}\)
mà \(\dfrac{1}{25}>\dfrac{1}{27}\)
nên \(\left(\dfrac{1}{5}\right)^{50}>\left(\dfrac{1}{3}\right)^{75}\)
9: \(\left(-\dfrac{1}{2}\right)^{300}=\left(\dfrac{1}{2}\right)^{300}=\left(\dfrac{1}{8}\right)^{100}=\dfrac{1}{8^{100}}\)
\(\left(-\dfrac{1}{3}\right)^{200}=\left(\dfrac{1}{3}\right)^{200}=\dfrac{1}{3^{200}}=\dfrac{1}{9^{100}}\)
mà \(\dfrac{1}{8^{100}}>\dfrac{1}{9^{100}}\left(8^{100}< 9^{100}\right)\)
nên \(\left(-\dfrac{1}{2}\right)^{300}>\left(-\dfrac{1}{3}\right)^{200}\)
10: \(\left(\dfrac{1}{16}\right)^{30}=\dfrac{1}{16^{30}}=\dfrac{1}{\left(2^4\right)^{30}}=\dfrac{1}{2^{120}}\)
\(\left(\dfrac{1}{8}\right)^{20}=\dfrac{1}{8^{20}}=\dfrac{1}{2^{60}}\)
mà \(\dfrac{1}{2^{120}}< \dfrac{1}{2^{60}}\left(2^{120}>2^{60}\right)\)
nên \(\left(\dfrac{1}{16}\right)^{30}< \left(\dfrac{1}{8}\right)^{20}\)
11; \(\left(\dfrac{1}{16}\right)^{11}=\dfrac{1}{16^{11}}=\dfrac{1}{\left(2^4\right)^{11}}=\dfrac{1}{2^{44}}\)
\(\left(\dfrac{1}{32}\right)^9=\dfrac{1}{32^9}=\dfrac{1}{\left(2^5\right)^9}=\dfrac{1}{2^{45}}\)
mà \(\dfrac{1}{2^{44}}>\dfrac{1}{2^{45}}\left(2^{44}< 2^{45}\right)\)
nên \(\left(\dfrac{1}{16}\right)^{11}>\left(\dfrac{1}{32}\right)^9\)
12: \(\left(\dfrac{1}{32}\right)^6=\left[\left(\dfrac{1}{2}\right)^5\right]^6=\left(\dfrac{1}{2}\right)^{30}=\dfrac{1}{2^{30}}\)
\(\left(\dfrac{1}{16}\right)^7=\left[\left(\dfrac{1}{2}\right)^4\right]^7=\left(\dfrac{1}{2}\right)^{28}=\dfrac{1}{2^{28}}\)
mà \(\dfrac{1}{2^{30}}< \dfrac{1}{2^{28}}\left(2^{30}>2^{28}\right)\)
nên \(\left(\dfrac{1}{32}\right)^6< \left(\dfrac{1}{16}\right)^7\)