So sánh

a) Do 2>1 và 24 > 16 => $2^{24} > 2^{16}$

b) Ta có: $(- \frac{1}{5})^{300} = [(- \frac{1}{5})^{3}]^{100} = (- \frac{1}{125})^{100} = (\frac{1}{125})^{100}$

$(- \frac{1}{3})^{500} = [(- \frac{1}{3})^{5}]^{100} = (- \frac{1}{243})^{100} = (\frac{1}{243})^{100}$

Do $\frac{1}{125} > \frac{1}{243} > 0$ nên $(\frac{1}{125})^{100} > (\frac{1}{243})^{100} .$

Vậy $(- \frac{1}{5})^{300} > (- \frac{1}{3})^{500}$

c) Do $\frac{32}{17} > 1 > 0$ nên $(\frac{32}{17})^{15} > 1.$ Mặt khác, $0 < \frac{17}{32} < 1$ nên $(\frac{17}{32})^{30} < 1.$

Vậy $(\frac{32}{17})^{15} > (\frac{17}{32})^{30} .$