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The given expression is:

\[
\left( -7^{12} \right)^{-3}
\]

We are asked to simplify this expression using the laws of exponents.

### Steps:

1. **Apply the power rule for exponents:** 
   \[
   \left( a^m \right)^n = a^{m \cdot n}
   \]
   Applying this rule to the expression:
   \[
   \left( -7^{12} \right)^{-3} = -7^{12 \cdot (-3)} = -7^{-36}
   \]

2. **Simplify further using the negative exponent rule:** 
   The negative exponent rule states that:
   \[
   a^{-n} = \frac{1}{a^n}
   \]
   Thus:
   \[
   -7^{-36} = -\frac{1}{7^{36}}
   \]

The simplified expression is:

\[
-\frac{1}{7^{36}}
\]

Let me know if you need further clarification or if you'd like to explore additional concepts related to this problem!

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Here are 5 related questions to deepen your understanding:

1. How do you simplify an expression with multiple exponents, like \((a^m)^n\)?
2. What happens when the base of the exponent is negative, such as in \((-a)^m\)?
3. How do you simplify expressions like \((a^m \cdot b^n)^p\)?
4. What is the significance of the zero exponent in expressions like \(a^0\)?
5. How do you convert between exponential notation and radical notation?

**Tip:** Always remember that negative exponents represent the reciprocal of the base raised to the corresponding positive exponent!

Learn how to simplify the expression ( -7^12 )^{-3} using the laws of exponents. This problem covers concepts like negative exponents and the power of a power rule. Suitable for students in Grades 7-9.

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