To solve the expressions given in the image, let's evaluate each part individually:

1. **Expression a:**

\[
\frac{5 \cdot 4^{15} \cdot 27^6 - 4 \cdot 3^{20} \cdot 9^7}{15 \cdot 2^{20} \cdot 6^{18} - 7 \cdot 2^{29} \cdot 9^9}
\]

This expression involves high powers and can be simplified generally. The approach is to simplify the terms by reducing the powers where possible using the properties of exponents. However, because of the scale of the problem, calculating it by hand or without computational help is complex.

2. **Expression b:**

\[
\frac{3}{2} \cdot \frac{5}{4} \cdot \frac{9}{8} \cdot \ldots = \frac{1025}{1024}
\]

This appears to be a geometric series or sequence perhaps. Without the clear expression for what part of the sequence reaches 1025/1024, it's assumed that this is likely converging based on formula knowledge or simplifications.

For precise calculations of these kinds of expressions, using a computer algebra system or calculator is recommended to manage the large numbers and precise operations involved.