Let's solve the expression step by step.
The expression is:
\[ 81 \times \left(\frac{1}{3}\right)^4 - 0.05 \times (-10)^2 \]
Calculate \(\left(\frac{1}{3}\right)^4\): \[ \left(\frac{1}{3}\right)^4 = \frac{1^4}{3^4} = \frac{1}{81} \]
Now substitute this back into the expression: \[ 81 \times \frac{1}{81} - 0.05 \times (-10)^2 \]
Calculate \(81 \times \frac{1}{81}\): \[ 81 \times \frac{1}{81} = 1 \]
Next, calculate \((-10)^2\): \[ (-10)^2 = 100 \]
Now substitute this result back into the expression: \[ 1 - 0.05 \times 100 \]
Calculate \(0.05 \times 100\): \[ 0.05 \times 100 = 5 \]
Finally, subtract: \[ 1 - 5 = -4 \]
The final result is:
\[ \boxed{-4} \]