1. **State the problem:** Calculate the sum of $50.57 \times 10^3$ and $25.354 \times 10^3$. 2. **Formula and rules:** When adding numbers in scientific notation with the same power of 10, add the coefficients and keep the power of 10 the same. 3. **Intermediate work:** $$ (50.57 \times 10^3) + (25.354 \times 10^3) = (50.57 + 25.354) \times 10^3 $$ $$ = 75.924 \times 10^3 $$ 4. **Final answer:** $$ 75.924 \times 10^3 = 75,924 $$ So, the sum is $75,924$.