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Let's solve the problem step by step.

### Given:
We need to find the value of \( 3^{-3} \).

### Step 1: Rewrite the expression using the negative exponent rule.
The negative exponent rule states:
\[
a^{-n} = \frac{1}{a^n}
\]

Using this rule:
\[
3^{-3} = \frac{1}{3^3}
\]

### Step 2: Evaluate \( 3^3 \).
\[
3^3 = 3 \times 3 \times 3 = 27
\]

### Step 3: Write the final value.
\[
3^{-3} = \frac{1}{27}
\]

So, the value of \( 3^{-3} \) is \( \frac{1}{27} \).

Would you like more details on any part of this solution?

### 5 Related Questions:
1. How do you handle exponents with negative bases, such as \( (-3)^{-3} \)?
2. What is the general rule for simplifying fractional exponents?
3. Can you explain how to calculate \( 5^{-2} \)?
4. What happens when you raise a number to the power of zero, like \( 3^0 \)?
5. How would you approach \( 3^{-4} \), and what is its value?

**Tip:** When you encounter negative exponents, remember to flip the base to its reciprocal, then calculate the positive exponent.

Discover how to solve for 3^-3 by applying the negative exponent rule. This solution includes step-by-step calculations and the key concepts of exponents and reciprocals. Perfect for students in Grades 6-8.

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