1. **State the problem:** Calculate the value of $$B = 5^3 - 10^2 \times (3^4 - 2^4 \times 5)^{13}$$. 2. **Recall the order of operations:** We must evaluate exponents first, then multiplication and subtraction. 3. **Calculate each component:** - Calculate $$5^3 = 125$$. - Calculate $$10^2 = 100$$. - Calculate $$3^4 = 81$$. - Calculate $$2^4 = 16$$. 4. **Evaluate inside the parentheses:** - Calculate $$2^4 \times 5 = 16 \times 5 = 80$$. - Calculate $$3^4 - 2^4 \times 5 = 81 - 80 = 1$$. 5. **Raise the result to the 13th power:** - Since $$1^{13} = 1$$, this simplifies the expression. 6. **Substitute back and simplify:** - $$B = 125 - 100 \times 1 = 125 - 100 = 25$$. **Final answer:** $$B = 25$$.