Question

Answer 1

a) \(1024^9=\left(2^{10}\right)^9=2^{90}\)

Mà: \(2^{90}< 2^{100}\Rightarrow1024^9< 2^{100}\)

b) \(6\cdot5^{29}=\left(5+1\right)\cdot5^{29}=5^{30}+5^{29}\)

Mà: \(5^{30}< 5^{30}+5^{29}\)

\(\Rightarrow5^{30}< 6\cdot5^{29}\)

c) \(9^{49}=\left(3^2\right)^{49}=3^{98}\)

Mà: \(3^{98}>2^{98}\Rightarrow9^{49}>2^{98}\)

d) \(10^{30}=\left(10^3\right)^{10}=1000^{10}\)

\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

Mà: \(1024^{10}>1000^{10}\)

\(\Rightarrow10^{30}< 2^{100}\)