a)290 và 536
\(2^{90}=2^{5.18}=\left(2^5\right)^{18}=32^{18}\)
\(5^{36}=5^{2.18}=\left(5^2\right)^{18}=25^{18}\)
Vì \(32>25\)
Nên \(32^{18}>25^{18}\)
Vậy \(2^{90}>5^{36}\)
b) 227 và 318
\(2^{27}=2^{3.9}=\left(2^3\right)^9=8^9\)
\(3^{18}=3^{2.9}=\left(3^2\right)^9=9^9\)
Vì \(8< 9\)
Nên \(8^9< 9^9\)
Vậy \(2^{27}< 3^{18}\)
\(\left\{{}\begin{matrix}2^{90}=\left(2^{10}\right)^9=1024^9\\5^{36}=\left(5^4\right)^9=625^9\end{matrix}\right.\Leftrightarrow2^{90}>5^{36}\)
\(\left\{{}\begin{matrix}2^{27}=\left(2^3\right)^9=8^9\\3^{18}=\left(3^2\right)^9=9^9\end{matrix}\right.\Leftrightarrow2^{27}< 3^{18}\)
a,
\(2^{90}=2^{5.18}=\left(2^5\right)^{18}=32^{18}\)
\(5^{36}=5^{2.18}=\left(5^2\right)^{18}=25^{18}\)
Vì \(32^{18}>25^{18}\rightarrow2^{90}>5^{36}\)
b,
\(2^{27}=2^{3.9}=\left(2^3\right)^9=8^9\)
\(3^{18}=3^{2.9}=\left(3^2\right)^9=9^9\)
Vì\(8^9< 9^9\rightarrow2^{27}< 3^{18}\)