To evaluate the expression \( 7 \div\left[2 \times(4-3) \div\left(4^2+4\right)\right] \div 2 \), we will proceed step by step and round the answer to three decimal places.
1. Evaluate the inner parentheses:
[tex]\[
4 - 3 = 1
\][/tex]
So, the expression becomes \( 7 \div\left[2 \times 1 \div\left(4^2+4\right)\right] \div 2 \).
2. Evaluate the exponent inside the parentheses:
[tex]\[
4^2 = 16
\][/tex]
So, the expression becomes \( 7 \div\left[2 \times 1 \div\left(16+4\right)\right] \div 2 \).
3. Evaluate the addition inside the parentheses:
[tex]\[
16 + 4 = 20
\][/tex]
So, the expression becomes \( 7 \div\left[2 \times 1 \div 20\right] \div 2 \).
4. Evaluate the division inside the parentheses:
[tex]\[
1 \div 20 = 0.05
\][/tex]
So, the expression becomes \( 7 \div\left[2 \times 0.05\right] \div 2 \).
5. Evaluate the multiplication inside the parentheses:
[tex]\[
2 \times 0.05 = 0.1
\][/tex]
So, the expression becomes \( 7 \div 0.1 \div 2 \).
6. Evaluate the first division:
[tex]\[
7 \div 0.1 = 70
\][/tex]
So, the expression becomes \( 70 \div 2 \).
7. Evaluate the final division:
[tex]\[
70 \div 2 = 35
\][/tex]
Therefore, the final answer, rounded to three decimal places, is:
[tex]\[
\boxed{35.000}
\][/tex]
