Simplify 4^-2 × 4^-4: Negative Exponents Multiplication

Simplify the following equation:

$4^{-2}\times4^{-4}=$

To solve this problem, we'll follow these steps:

• Step 1: Identify that both terms have the same base, which is 4.

• Step 2: Use the exponent rule for multiplication of powers with the same base: $a^m \times a^n = a^{m+n}$.

• Step 3: Add the exponents $-2$ and $-4$.

Now, let's work through these steps:

Step 1: We have the expression $4^{-2} \times 4^{-4}$.

Step 2: Applying the exponent rule, we combine the exponents:

$4^{-2} \times 4^{-4} = 4^{-2 + (-4)}$

Therefore, our answer is $4^{-2-4}$, which matches choice 4.