Question

So sánh

A) (-1/16) ^ 1000 và (-1/2) ^ 5000 

B) 3^400 va 4^300.  mìh cần gắp lắm giải giùm mìh vs mìh tick cho lẹ đi :))

Answer 1

a/

\(\left(-\frac{1}{16}\right)^{1000}=\left(-\frac{1}{2^4}\right)^{1000}=\left(-\frac{1}{2}\right)^{4000}.\)

Do \(\left(\frac{1}{2}\right)^{4000}>\left(\frac{1}{2}\right)^{5000}\Rightarrow\left(-\frac{1}{2}\right)^{4000}< \left(-\frac{1}{2}\right)^{5000}\Rightarrow\left(-\frac{1}{16}\right)^{1000}< \left(-\frac{1}{2}\right)^{5000}\)

b/

\(3^{400}=\left(3^4\right)^{100}=81^{100}\)

\(4^{300}=\left(4^3\right)^{100}=64^{100}\)

\(\Rightarrow81^{100}>64^{100}\Rightarrow3^{400}>4^{300}\)