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

Question

Simplify the following equation:

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

00:00 Simplify the following problem

00:03 According to the laws of exponents, the multiplication of powers with an equal base (A)

00:06 equals the same base raised to the sum of the exponents (N+M)

00:09 We will apply this formula to our exercise

00:13 Note that we are adding together negative numbers

00:17 A positive x A negative is always negative, therefore we subtract as follows

00:23 This is the solution

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.

$4^{-2-4}$