Simplify (4×a)^(-x): Negative Exponent Expression

Great question! The negative exponent only tells us to flip the base to the denominator - it doesn't make the result negative. Think of it as a direction: move the base from numerator to denominator (or vice versa).

Yes! When you have $(4 \times a)^{-x}$, the exponent -x applies to the entire product. Use the Power of Product Rule: $(4 \times a)^{-x} = 4^{-x} \times a^{-x}$.

You can write it as $\frac{1}{4^x \times a^x}$ or $\frac{1}{(4a)^x}$ - both are correct! The first form shows each factor clearly, while the second uses the Power of Product Rule in reverse.

If we had $(4 \times a)^x$, it would simply equal $4^x \times a^x$. The negative exponent is what creates the fraction by moving everything to the denominator.

Substitute back! If your answer is $\frac{1}{4^x \times a^x}$, verify that this equals $(4 \times a)^{-x}$ by applying the rules in reverse. Both expressions should represent the same value.