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The question is asking to determine the coefficient of the constant term in the binomial expansion of the expression:

\[
\left( x^3 - \frac{3}{x^2} \right)^5.
\]

### Step-by-step Solution:

1. **General Binomial Expansion**:
   The binomial theorem for expanding \((a + b)^n\) is:

   \[
   (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k.
   \]

   In this case, we have \( a = x^3 \) and \( b = -\frac{3}{x^2} \), and \( n = 5 \).

2. **Find Constant Term**:
   A constant term will be found when the powers of \(x\) in both terms cancel out, i.e., when the total exponent of \(x\) becomes zero.

   We need to find terms in the expansion where:

   \[
   (x^3)^{5-k} \left(-\frac{3}{x^2}\right)^k
   \]

   results in no \(x\)-terms, meaning:

   \[
   3(5-k) - 2k = 0.
   \]

3. **Solve for \(k\)**:
   \[
   15 - 3k - 2k = 0 \implies 15 = 5k \implies k = 3.
   \]

4. **Find the Corresponding Coefficient**:
   For \(k = 3\), the corresponding term in the expansion is:

   \[
   \binom{5}{3} (x^3)^{5-3} \left(-\frac{3}{x^2}\right)^3.
   \]

   Simplifying this:

   \[
   \binom{5}{3} (x^3)^2 \left(-\frac{3}{x^2}\right)^3 = \binom{5}{3} x^6 \left(-\frac{27}{x^6}\right).
   \]

   The powers of \(x\) cancel out, leaving:

   \[
   \binom{5}{3} (-27).
   \]

   The binomial coefficient \(\binom{5}{3} = 10\), so the coefficient of the constant term is:

   \[
   10 \times (-27) = -270.
   \]

### Final Answer:
The coefficient of the constant term is **-270**.

---

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### Related Questions:
1. How does the binomial theorem work for higher powers?
2. How do you compute binomial coefficients?
3. What are the general conditions for finding constant terms in a binomial expansion?
4. Can we expand the binomial for fractional exponents?
5. How would the expansion change if we had a different exponent (e.g., 6 instead of 5)?

### Tip:
When looking for constant terms in binomial expansions, always focus on how the powers of variables cancel out.

Betrakta binomialutvecklingen (x^3 - 3/x^2)^5. Bestäm koefficienten för den konstanta termen i denna binomialutveckling.

Explore how to find the coefficient of the constant term in the binomial expansion of (x^3 - 3/x^2)^5. This problem focuses on key concepts in binomial expansion and exponent rules, suitable for students in Grades 10-12.

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