Sure, let's solve the expression step by step.
The given mathematical expression is:
[tex]\[ 4 \times \left(56 \div 2^3\right) + 6^2 + 10^2 \times 5 - 4 \][/tex]
We’ll break it down into parts and calculate each part separately, then combine them in the final step.
1. Evaluate the exponentiation inside the parentheses:
[tex]\[ 2^3 = 8 \][/tex]
2. Divide 56 by the result of step 1:
[tex]\[ 56 \div 8 = 7.0 \][/tex]
3. Multiply the result by 4:
[tex]\[ 4 \times 7.0 = 28.0 \][/tex]
4. Calculate the exponentiation for the next term:
[tex]\[ 6^2 = 36 \][/tex]
5. Calculate the exponentiation and multiplication for the next term:
[tex]\[ 10^2 = 100 \][/tex]
[tex]\[ 100 \times 5 = 500 \][/tex]
6. Combine all the results and perform the addition and subtraction:
The expression now looks like this:
[tex]\[ 28.0 + 36 + 500 - 4 \][/tex]
Now, we sum these intermediate results:
[tex]\[ 28.0 + 36 = 64.0 \][/tex]
[tex]\[ 64.0 + 500 = 564.0 \][/tex]
Then, subtract 4:
[tex]\[ 564.0 - 4 = 560.0 \][/tex]
So, the final result of the given expression is [tex]\(\boxed{560.0}\)[/tex].
