To simplify the expression \(-3^{-3} / 6^{-2}\), follow these steps:

1. **Apply the negative exponents**:
   \[
   a^{-n} = \frac{1}{a^n}
   \]
   So:
   \[
   -3^{-3} = -\frac{1}{3^3} = -\frac{1}{27}
   \]
   and
   \[
   6^{-2} = \frac{1}{6^2} = \frac{1}{36}
   \]

2. **Rewrite the expression**:
   \[
   \frac{-1/27}{1/36}
   \]

3. **Divide the fractions**: To divide by a fraction, multiply by its reciprocal:
   \[
   \frac{-1}{27} \times \frac{36}{1} = \frac{-1 \times 36}{27 \times 1} = \frac{-36}{27}
   \]

4. **Simplify**:
   \[
   \frac{-36}{27} = -\frac{36}{27} = -\frac{4}{3}
   \]

The simplified expression is:
\[
\boxed{-\frac{4}{3}}
\]

Would you like further details or explanations?

Here are 5 related questions:
1. How do you simplify expressions with negative exponents?
2. What is the rule for dividing fractions?
3. How

Learn how to simplify the expression -3^-3 / 6^-2 using the properties of negative exponents and fraction operations. This problem involves applying exponent rules and dividing fractions step-by-step. Suitable for students in Grades 8-10.

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