1. **State the problem:** Calculate the difference between $8.75 \times 10^4$ and $5.34 \times 10^4$. 2. **Formula and rules:** When subtracting numbers in scientific notation with the same power of 10, subtract the coefficients and keep the power of 10 the same. 3. **Intermediate work:** $$8.75 \times 10^4 - 5.34 \times 10^4 = (8.75 - 5.34) \times 10^4$$ $$= 3.41 \times 10^4$$ 4. **Explanation:** Since both terms have the same exponent $10^4$, we subtract the decimal parts $8.75 - 5.34 = 3.41$ and keep the $10^4$ factor. 5. **Final answer:** $$3.41 \times 10^4$$