Question

so sánh (1/2)^24 và (1/3)^36

Answer 1

\(\left(\dfrac{1}{2}\right)^{24}=\left[\left(\dfrac{1}{2}\right)^2\right]^{12}=\left(\dfrac{1}{4}\right)^{12}\\ \left(\dfrac{1}{3}\right)^{36}=\left[\left(\dfrac{1}{3}\right)^3\right]^{12}=\left(\dfrac{1}{27}\right)^{12}\\ Vì:\dfrac{1}{4}>\dfrac{1}{27}\Rightarrow\left(\dfrac{1}{4}\right)^{12}>\left(\dfrac{1}{27}\right)^{12}\Rightarrow\left(\dfrac{1}{2}\right)^{24}>\left(\dfrac{1}{3}\right)^{36}\)

Answer 2

Dễ thấy \(2^{24}< 3^{36}\Rightarrow\dfrac{1}{2^{24}}>\dfrac{1}{3^{36}}\)

Answer 3

(1/2)^24=[(1/2)^2]^12=(1/4)^12

(1/3)^36=[(1/3)^3]^12=(1/27)^12

mà 1/4>1/27

nên (1/2)^24>(1/3)^36