1. Given the problem: Calculate $6400 \times 2.7$ using the known multiplication $64 \times 27 = 1728$. 2. Observe that $6400$ can be written as $64 \times 100$ and $2.7$ can be written as $\frac{27}{10}$. 3. Substitute these expressions into the multiplication: $$6400 \times 2.7 = (64 \times 100) \times \frac{27}{10}$$ 4. Rearrange the terms using associativity of multiplication: $$= 64 \times 27 \times \frac{100}{10}$$ 5. From the given, $64 \times 27 = 1728$, so: $$= 1728 \times 10$$ 6. Multiply: $$1728 \times 10 = 17280$$ 7. Therefore, the result is $6400 \times 2.7 = 17280$.