Simplify the Product: Negative 4 Raised to Powers 3, 4, and 2

The negative sign is part of the base $-4$, not a separate factor. When we multiply $-4^3 \times -4^4 \times -4^2$, we're multiplying three expressions with the same base $-4$.

Add exponents when you're multiplying expressions with the same base. Since all three terms have base $-4$, we use the rule $a^m \times a^n = a^{m+n}$.

That's a common error! Remember that $-4$ is the complete base, not just 4. The negative sign stays with the base throughout the calculation, so the final answer is $-4^9$.

Not usually! The simplified form $-4^9$ is the complete answer. Computing $-4^9 = -262,144$ isn't necessary unless specifically requested.

That would mean $\frac{1}{4^9}$, which is completely different! We're adding positive exponents (3+4+2=9), not subtracting them. The base stays $-4$ throughout.