Evaluate $$ y=3^{x} $$, when $$ x=-4 $$

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To evaluate $$ y = 3^{x} $$ when $$ x = -4 $$, follow these steps:

1. **Substitute the value of $$ x $$:**
   
   $$
   y = 3^{-4}
   $$

2. **Understand Negative Exponents:**
   
   A negative exponent indicates that you take the reciprocal of the base raised to the positive exponent. In general:
   
   $$
   a^{-n} = \frac{1}{a^{n}}
   $$
   
   Applying this to our equation:
   
   $$
   y = \frac{1}{3^{4}}
   $$

3. **Calculate $$ 3^{4} $$:**
   
   $$
   3^{4} = 3 \times 3 \times 3 \times 3 = 81
   $$

4. **Final Calculation:**
   
   $$
   y = \frac{1}{81}
   $$

**Answer:**  
When $$ x = -4 $$, $$ y = \frac{1}{81} $$.
When $$ x = -4 $$, $$ y = \frac{1}{81} $$.

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