Let's solve the given mathematical expression step by step:
[tex]\[ 402 \div (462 - 261) + 32 + 5 - 6^2 \][/tex]
### Step 1: Evaluate the expression inside the parentheses
First, handle the operation inside the parentheses:
[tex]\[ 462 - 261 = 201 \][/tex]
So the expression now looks like:
[tex]\[ 402 \div 201 + 32 + 5 - 6^2 \][/tex]
### Step 2: Perform the division
Next, divide 402 by the result obtained from the parentheses:
[tex]\[ 402 \div 201 = 2.0 \][/tex]
Now the expression is:
[tex]\[ 2.0 + 32 + 5 - 6^2 \][/tex]
### Step 3: Perform the exponentiation
Calculate [tex]\( 6^2 \)[/tex]:
[tex]\[ 6^2 = 36 \][/tex]
So the expression updates to:
[tex]\[ 2.0 + 32 + 5 - 36 \][/tex]
### Step 4: Sequentially perform the additions and subtraction
Now, add and subtract the remaining terms in left-to-right order:
[tex]\[ 2.0 + 32 = 34.0 \][/tex]
[tex]\[ 34.0 + 5 = 39.0 \][/tex]
[tex]\[ 39.0 - 36 = 3.0 \][/tex]
### Final Result
The value of the given mathematical expression is:
[tex]\[ 3.0 \][/tex]
So the final result is:
[tex]\[ 402 \div (462 - 261) + 32 + 5 - 6^2 = 3.0 \][/tex]
