[tex]\displaystyle\\
2,25\times 2,25^3\times 2,25^5\times \cdots\times 2,25^{101}=\\\\
=2,25^1\times 2,25^3\times 2,25^5\times \cdots\times 2,25^{101}=\\\\
=2,25^{1+3+5+ \cdots + 101}\\\\
\text{Calculam numarul de termeni ai sirului de la exponent:}\\\\
n= \frac{101-1}{2}+1 = \frac{100}{2}+1 =50+1 = 51 \text{ de termeni} \\ \\
2,25^{1+3+5+ \cdots + 101} = 2,25^{ \frac{51(101+1)}{2} } = 2,25^{ \frac{51(102)}{2} } =2,25^{ 51\times 51} =\boxed{2,25^{2601}}[/tex]
