To convert the expression \(3^{-4}\) to a decimal or numerical value, you first evaluate the exponent. The negative exponent means that you take the reciprocal of the base raised to the positive exponent:
\[ 3^{-4} = \frac{1}{3^4} \]
Now, calculate \(3^4\):
\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]
So we have:
\[ 3^{-4} = \frac{1}{81} \]
This can also be represented as a decimal:
\[ \frac{1}{81} \approx 0.012345679 \]
Thus, \(3^{-4} \approx 0.0123\) when rounded to four decimal places.