a/ \(2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(3^{200}=\left(3^2\right)^{100}=9^{100}\)
Vì \(8^{100}< 9^{100}\Leftrightarrow2^{300}< ^{200}\)
b/ \(3^{450}=\left(3^3\right)^{150}=27^{150}\)
\(5^{300}=\left(5^2\right)^{300}=25^{150}\)
Vì \(27^{150}>25^{100}\Leftrightarrow3^{450}>5^{300}\)
a) ta có:
\(2^{300}=\left(2^3\right)^{100}=8^{100}\\ 3^{200}=\left(3^2\right)^{100}=9^{100}\)
ta thấy: \(9^{100}>8^{100}\) nên \(2^{300}< 3^{200}\)
vậy \(2^{300}< 3^{200}\)
b) ta có:
\(3^{450}=\left(3^3\right)^{150}=27^{150}\\ 5^{300}=\left(5^2\right)^{150}=25^{150}\)
\(27^{150}>25^{150}\Rightarrow3^{450}>5^{300}\)
vậy \(3^{450}>5^{300}\)
Ta có :
2300=(23)100=8100
3200=(32)100=9100
Vì 8<9 nên 8100<9100
Vậy 2300<3200