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

To solve this problem, we will use the rules for handling exponents:

• Step 1: Start with the original expression $(4 \times a)^{-x}$.

• Step 2: Apply the Power of a Product rule: $(4 \times a)^{-x} = 4^{-x} \times a^{-x}$.

• Step 3: Apply the Negative Exponent rule for each factor: $4^{-x} = \frac{1}{4^x}$ and $a^{-x} = \frac{1}{a^x}$.

• Step 4: Combine the results of Step 3, resulting in: $\frac{1}{4^x \times a^x}$.

The equivalent expression for $(4 \times a)^{-x}$ is $\frac{1}{4^x \times a^x}$.

By comparing this with the given choices, the correct answer choice is:

$\frac{1}{4^x \times a^x}$