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

Insert the corresponding expression:

$\left(4\times a\right)^{-x}=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, a number with a negative exponent (-N)

00:07 equals the reciprocal number with the same exponent multiplied by (-1)

00:10 We will apply this formula to our exercise

00:16 Convert to the reciprocal number

00:20 Raise to the same power (N) multiplied by (-1)

00:27 According to the laws of exponents, a multiplication raised to a power (N)

00:30 equals the multiplication where each factor is raised to the same power (N)

00:33 We will apply this formula to our exercise

00:36 This is the solution

Step-by-Step Solution

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:

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