Question

1,So sánh

a,\(\left(\dfrac{-1}{8}\right)^{100}\)và\(\left(\dfrac{-1}{4}\right)^{200}\)

b,4¹⁰⁰và 2²⁰²

c,\(5^{2000}\)và \(10^{1000}\)

d,31⁵ và 17⁷

Answer 1

a)\(VT=\left(-\dfrac{1}{8}\right)^{100}=\dfrac{1}{8^{100}}=\dfrac{1}{\left(2^3\right)^{100}}=\dfrac{1}{2^{300}}\)

\(VP=\left(-\dfrac{1}{4}\right)^{200}=\dfrac{1}{\left(2^2\right)^{200}}=\dfrac{1}{2^{400}}\)

\(\Rightarrow VT>VP\)

b) \(VT=4^{100}=\left(2^2\right)^{100}=2^{200}< 2^{202}=VP\)

c) \(VT=5^{2000}=\left(5^2\right)^{1000}=25^{1000}>10^{1000}=VP\)

d) \(VT=31^5< 32^5=\left(2^5\right)^5=2^{25}\)

\(VP=17^7>16^7=\left(2^4\right)^7=2^{28}\)

\(VP>VT\)