\(a=2^{100}=\left(2^4\right)^{25}=16^{25}\)
\(b=3^{75}=\left(3^3\right)^{25}=27^{25}\)
\(c=5^{50}=\left(5^2\right)^{25}=25^{25}\)
Vì \(16^{25}< 25^{25}< 27^{25}\)
\(\Rightarrow a< c< b\)
\(a=2^{100},b=3^{75},c=5^{50}\\ \Rightarrow a=30^{85},b=30^{65},c=30^{44}\\ \Rightarrow a>b>c\)
Ta có:
\(a=2^{100}=2^{4\cdot25}=\left(2^4\right)^{25}=16^{25}\)
\(b=3^{75}=3^{3\cdot25}=\left(3^3\right)^{25}=27^{25}\)
\(c=5^{50}=5^{2\cdot25}=\left(5^2\right)^{25}=25^{50}\)
Ta thấy:
\(16< 25< 27\)
\(\Rightarrow16^{25}< 25^{25}< 27^{25}\)
\(\Rightarrow2^{100}< 5^{50}< 3^{75}\)
\(\Rightarrow a< c< b\)
