Answer :
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]
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]
