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.