Solve: 4^(-6) × 4 Using Negative Exponent Rules

Insert the corresponding expression:

$4^{-6}\times4=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:04 According to the laws of exponents, multiplying powers with the same base (A)

00:07 equals the same base raised to the sum of the exponents (N+M)

00:10 Any number raised to the power of 1 is always equals itself

00:13 We'll apply this formula to our exercise, and raise to the power of 1

00:18 Now let's apply the second formula

00:21 We'll maintain the base and add the exponents together

00:31 According to the laws of exponents, any number with a negative exponent (-N)

00:35 equals its reciprocal raised to the opposite exponent (N)

00:38 We'll apply this formula to our exercise

00:41 We'll convert it to the reciprocal and raise it to the opposite exponent

00:44 This is the solution

Step-by-Step Solution

To simplify the expression $4^{-6} \times 4$ , follow these steps:

Step 1: Apply the rule for multiplying powers with the same base, which is $a^m \times a^n = a^{m+n}$ .
Step 2: Identify the exponents for the terms. Here, we have $4^{-6}$ and $4^1$ , implying $m = -6$ and $n = 1$ .
Step 3: Add the exponents: $(-6) + 1 = -5$ . Thus, we have $4^{-6} \times 4^1 = 4^{-5}$ .
Step 4: Recognize that a negative exponent indicates a reciprocal. Therefore, $4^{-5} = \frac{1}{4^5}$ .

Therefore, the solution to the expression $4^{-6} \times 4$ is $\frac{1}{4^5}$ .