Simplify: $839478 \times 625$

### Concept & Formula Multiplying by powers of 5 (like $5, 25, 125, 625$) can be simplified by converting the multiplier into a fraction based on powers of 10. We know that $625 = 5^4$. We can rewrite this as $(\frac{10}{2})^4 = \frac{10000}{16}$. ### Step-by-Step Solution * **Calculation:** Substitute $625$ with its equivalent fraction $\frac{10000}{16}$: $$ 839478 \times \left(\frac{10}{2}\right)^4 $$ $$ 839478 \times \frac{10000}{16} $$ * Multiply the numerator first (append four zeros): $$ \frac{8394780000}{16} $$ * Divide by $16$ (or divide by $2$ four consecutive times): $$ \frac{8394780000}{16} = 524673750 $$ ### Exam Strategy & Shortcut Whenever multiplying by $625$, append four zeros to the end of the number and divide the result by 16. Dividing by 16 is often much faster and less error-prone than doing a 3-digit multiplication, especially if you halve the number four times in your head. ### Common Pitfall Students often miss the power-of-10 conversion and try to multiply by 625 directly. While doable, it creates three separate massive lines of addition which eats up valuable time in competitive exams. ### Final Answer Therefore, the correct answer is **524673750**.