Step 1 :First, we need to follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division, and Addition and Subtraction. We will start by solving the expressions inside the brackets and parentheses.
Step 2 :Let's first solve the expressions inside the parentheses: \((8-7) = 1\) and \((4-5) = -1\)
Step 3 :Now the expression becomes: \(21-\{8-5[6\ 4(1)-9(-1)]-10+25 \times 2+13\}\)
Step 4 :Next, we will solve the expression inside the square brackets: \(6\ 4(1)-9(-1) = 6 \times 4 + 9 = 24 + 9 = 33\)
Step 5 :Now the expression becomes: \(21-\{8-5[33]-10+25 \times 2+13\}\)
Step 6 :Now, we will solve the expression inside the curly brackets: \(8-5[33]-10+25 \times 2+13 = 8 - 5 \times 33 - 10 + 25 \times 2 + 13\)
Step 7 :Following the order of operations, we will perform multiplication first: \(8 - 165 - 10 + 50 + 13\)
Step 8 :Now, we will perform addition and subtraction from left to right: \(-157 - 10 + 50 + 13 = -167 + 50 + 13 = -117 + 13 = -104\)
Step 9 :Now the expression becomes: \(21 - (-104)\)
Step 10 :Finally, we will perform the subtraction: \(21 - (-104) = 21 + 104 = 125\)
Step 11 :Final Answer: \(\boxed{125}\)