The given expression is:

\[
\frac{-21a^2b^2}{28a^3b^3}
\]

Let's simplify this step by step:

1. **Simplify the coefficients**: 
   The fraction involving the numerical part is \(\frac{-21}{28}\). We can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 7:
   \[
   \frac{-21}{28} = \frac{-21 \div 7}{28 \div 7} = \frac{-3}{4}
   \]

2. **Simplify the variables \(a\)**:
   We have \(a^2\) in the numerator and \(a^3\) in the denominator. Using the rule \(\frac{a^m}{a^n} = a^{m-n}\), we subtract the exponents:
   \[
   \frac{a^2}{a^3} = a^{2-3} = a^{-1} = \frac{1}{a}
   \]

3. **Simplify the variables \(b\)**:
   Similarly, we have \(b^2\) in the numerator and \(b^3\) in the denominator:
   \[
   \frac{b^2}{b^3} = b^{2-3} = b^{-1} = \frac{1}{b}
   \]

4. **Final expression**:
   Putting it all together, we get:
   \[
   \frac{-3}{4a b}
   \]

So, the simplified form of \(\frac{-21a^2b^2}{28a^3b^3}\) is:

\[
\boxed{\frac{-3}{4ab}}
\]

Would you like further details or have any questions?

Here are some related problems to expand on this:

1. Simplify \(\frac{15x^4y^2}{25x^6y^3}\).
2. Simplify \(\frac{-12a^5b^4}{18a^3b^2}\).
3. Simplify \(\frac{24m^3n^4}{36m^5n^2}\).
4. Simplify \(\frac{-50p^2q^5}{75p^4q^6}\).
5. Simplify \(\frac{49x^3y^2}{63x^5y^4}\).

**Tip:** When simplifying fractions involving exponents, remember to subtract exponents when dividing terms with the same base.

Learn how to simplify the expression -21a²b²/28a³b³ step by step. This problem involves key algebraic concepts such as simplifying rational expressions, exponent rules, and using the greatest common divisor (GCD) to simplify coefficients. Suitable for students in Grades 8-10.

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