To solve the ratio \( \frac{27^2}{25^3} \), we first need to calculate the values of \( 27^2 \) and \( 25^3 \).

1. Calculate \( 27^2 \):
\[ 27^2 = 27 \times 27 = 729 \]

2. Calculate \( 25^3 \):
\[ 25^3 = 25 \times 25 \times 25 = 625 \times 25 = 15625 \]

Now, we can form the ratio:
\[ \frac{27^2}{25^3} = \frac{729}{15625} \]

This fraction cannot be simplified further because 729 and 15625 do not have any common factors other than 1. Therefore, the ratio \( \frac{27^2}{25^3} \) is:
\[ \frac{729}{15625} \]