Sure, I will break down the solution using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
1. Evaluate the expression inside the parentheses:
Inside the parentheses, we first resolve the division:
[tex]\[
21 \div 3 = 7
\][/tex]
Then we add the result to 8:
[tex]\[
8 + 7 = 15
\][/tex]
So, the expression inside the parentheses simplifies to 15.
2. Multiply by 10 outside the parentheses:
[tex]\[
10 \times 15 = 150
\][/tex]
3. Addition outside the parentheses:
[tex]\[
5 + 150 = 155
\][/tex]
4. Raise the entire result to the power of 12:
[tex]\[
155^{12} = 1.923004843233764 \times 10^{26}
\][/tex]
Therefore, the final simplified value of the given expression is
[tex]\[
5+\left.10(8+21 \div 3) \quad\right|^{12} = 1.923004843233764 \times 10^{26}
\][/tex]
