Câu hỏi của tan suong Nguyen

Question

so sánh (1/9)20 và (1/27)13

Trần Đức Thắng · Accepted Answer

$\left(\frac{1}{9}\right)^{20}=\left(\left(\frac{1}{3}\right)^2\right)^{20}=\left(\frac{1}{3}\right)^{2.20}=\left(\frac{1}{3}\right)^{40}$$\left(\frac{1}{27}\right)^{13}=\left(\left(\frac{1}{3}\right)^3\right)^{13}=\left(\frac{1}{3}\right)^{3.13}=\left(\frac{1}{3}\right)^{39}$Vì 39 < 40 $\Leftrightarrow\left(\frac{1}{3}\right)^{39}>\left(\frac{1}{3}\right)^{40}$$\left(\frac{1}{27}\right)^{13}>\left(\frac{1}{9}\right)^{20}$Câu trả lời: $\left(\frac{1}{9}\right)^{20}=\left(\left(\frac{1}{3}\right)^2\right)^{20}=\left(\frac{1}{3}\right)^{2.20}=\left(\frac{1}{3}\right)^{40}$$\left(\frac{1}{27}\right)^{13}=\left(\left(\frac{1}{3}\right)^3\right)^{13}=\left(\frac{1}{3}\right)^{3.13}=\left(\frac{1}{3}\right)^{39}$Vì 39 < 40 $\Leftrightarrow\left(\frac{1}{3}\right)^{39}>\left(\frac{1}{3}\right)^{40}$$\left(\frac{1}{27}\right)^{13}>\left(\frac{1}{9}\right)^{20}$

Minh Triều · Answer

$\left(\frac{1}{9}\right)^{20}=\left[\left(\frac{1}{3}\right)^2\right]^{20}=\left(\frac{1}{3}\right)^{40}$$\left(\frac{1}{27}\right)^{13}=\left[\left(\frac{1}{3}\right)^3\right]^{13}=\left(\frac{1}{3}\right)^{39}$vì 40 > 39 nên $\left(\frac{1}{3}\right)^{40}>\left(\frac{1}{3}\right)^{39}$hay $\left(\frac{1}{9}\right)^{20}>\left(\frac{1}{27}\right)^{13}$Câu trả lời: $\left(\frac{1}{9}\right)^{20}=\left[\left(\frac{1}{3}\right)^2\right]^{20}=\left(\frac{1}{3}\right)^{40}$$\left(\frac{1}{27}\right)^{13}=\left[\left(\frac{1}{3}\right)^3\right]^{13}=\left(\frac{1}{3}\right)^{39}$vì 40 > 39 nên $\left(\frac{1}{3}\right)^{40}>\left(\frac{1}{3}\right)^{39}$hay $\left(\frac{1}{9}\right)^{20}>\left(\frac{1}{27}\right)^{13}$

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