Let a₁, a₂ ........ a₁₀ be a G.P. . If $\frac{{\mathrm{a}}_3}{{\mathrm{a}}_1}=25$ then $\frac{{\mathrm{a}}_9}{{\mathrm{a}}_5}$ equals

Given that a₁, a₂ .......a₁₀ are in G.P.
let the common ratio be 'r'.
Given that $\frac{{\mathrm{a}}_3}{{\mathrm{a}}_1}=25\Rightarrow \frac{{\mathrm{a}}_1{\mathrm{r}}^2}{{\mathrm{a}}_1}=25\Rightarrow {\mathrm{r}}^2=25$
$\therefore \frac{a_9}{a_5}=\frac{{\mathrm{a}}_1{\mathrm{r}}^8}{{{\mathrm{a}}_1}^{ }{\mathrm{r}}^4}={\mathrm{r}}^4=5^4=625$