Solve: 4^(-6) × 4 Using Negative Exponent Rules

The multiplication rule for exponents says $a^m \times a^n = a^{m+n}$. You only multiply exponents when raising a power to another power, like $(a^m)^n = a^{mn}$.

First complete all exponent operations, then deal with negatives. Here: $4^{-6} \times 4^1 = 4^{-5}$, then convert $4^{-5} = \frac{1}{4^5}$.

That's exactly right! Any number without an exponent has an invisible exponent of 1. So $4 = 4^1$, making the addition clear: $-6 + 1 = -5$.

You could convert $4^{-6}$ to $\frac{1}{4^6}$ first, but it makes the problem much harder. It's much easier to use exponent rules first, then convert at the end!

Verify that $\frac{1}{4^5}$ equals the original expression. You can also check that $4^{-5} \times 4^5 = 4^0 = 1$, confirming our negative exponent conversion is correct.