**Core Concept**
Antipseudomonal penicillins are a class of beta-lactam antibiotics that exhibit enhanced activity against Pseudomonas aeruginosa, a Gram-negative bacterium responsible for various infections, particularly in immunocompromised patients. These antibiotics work by inhibiting cell wall synthesis in bacteria.

**Why the Correct Answer is Right**
The correct answer is **Carbenicillin**, a natural penicillin antibiotic that has been shown to exhibit significant activity against Pseudomonas aeruginosa. This is due to its ability to hydrolyze the bacterial penicillin-binding proteins (PBPs), leading to the disruption of cell wall synthesis and ultimately, bacterial cell death. Carbenicillin's antipseudomonal activity is attributed to its unique chemical structure, which allows it to effectively bind to the bacterial enzymes responsible for peptidoglycan synthesis.

**Why Each Wrong Option is Incorrect**
**Option A:** **Ampicillin** is a broad-spectrum penicillin, but it lacks significant activity against Pseudomonas aeruginosa and is therefore not considered an antipseudomonal penicillin.
**Option B:** **Piperacillin** is an extended-spectrum penicillin, but while it has some activity against Pseudomonas aeruginosa, it is not as potent as carbenicillin.
**Option C:** **Ticarcillin** is another extended-spectrum penicillin, but it is not as effective as carbenicillin against Pseudomonas aeruginosa.

**Clinical Pearl / High-Yield Fact**
When treating infections caused by Pseudomonas aeruginosa, it is essential to use antibiotics that have been specifically shown to exhibit antipseudomonal activity, such as carbenicillin. This is because Pseudomonas aeruginosa has developed significant resistance to many antibiotics, making it a challenging organism to treat.

**Correct Answer: C. Ticarcillin**