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

Insert the corresponding expression:

$4^{-6}\times4=$

Video Solution

Solution Steps

00:08 Let's simplify this problem step by step.

00:12 First, remember: When multiplying powers with the same base, like A,

00:18 we keep the base A and add the exponents, giving us A to the power of N plus M.

00:25 Also, any number to the power of one is just itself.

00:29 So, let's apply this: Our base raised to one stays the same.

00:34 Now, we'll use the second formula.

00:37 Keep the base and add those exponents together.

00:41 Remember: A negative exponent means the reciprocal.

00:45 It becomes its reciprocal raised to the positive exponent N.

00:50 Let's go ahead and apply this rule now.

00:53 Convert to the reciprocal and raise it to the opposite exponent.

00:58 And that's how we solve the problem. Great job!

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 $\frac{1}{4^5}$ .