Evaluate \( y=3^{x} \), when \( x=-4 \)

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 \( x = -4 \), \( y = \frac{1}{81} \).