It seems you've provided a variety of algebraic expressions and radical problems, including simplifying and rationalizing denominators, as well as expressions with variables. However, the notation appears a bit jumbled, making it difficult to interpret exactly what each part is referring to.

I can help by breaking down your questions based on what I think you're asking. It seems that you're asking for two main tasks:

1. Simplifying radical expressions (e.g., square roots, cube roots, etc.) and rationalizing denominators (removing any square roots or radicals from the denominator).
2. Simplifying algebraic expressions, particularly those with exponents and variables.

I'll need to reorganize the problem statements to clarify what needs to be solved. Could you please confirm or provide clarification? Here's how I understand the problems based on the format you've used:

Radical Expression Simplification & Rationalization

For example:

• Simplify and rationalize: $\frac{3}{\sqrt{5}}$
• Simplify and rationalize: $\frac{2}{\sqrt{7} - 3}$

These are typical of rationalizing the denominator in radical expressions.

Algebraic Expressions with Variables

For example:

• Simplify: $\frac{3x^2y}{\sqrt{25x^2y}}$
• Simplify: $\frac{-75a^5b^3}{\sqrt{5}}$

Would you like to focus on solving these specific examples or all of the types you've listed above? Let me know how you'd like to proceed!