Solve (9×2)^(-6): Negative Exponent Expression

Question

Insert the corresponding expression:

$\left(9\times2\right)^{-6}=$

00:00 Simplify the following problem

00:04 In order to open parentheses with a multiplication operation and an outside exponent

00:07 We raise each factor to the power

00:13 We'll apply this formula to our exercise

00:21 This is the solution

To solve this problem, we'll apply the power of a product rule for exponents:

Step 1: Identify the expression $(9 \times 2)^{-6}$ .
Step 2: Apply the power of a product rule, which states $(a \times b)^n = a^n \times b^n$ .
Step 3: Simplify the expression using the rule $(9 \times 2)^{-6} = 9^{-6} \times 2^{-6}$ .

By performing these steps, the expression $(9 \times 2)^{-6}$ becomes equivalent to $9^{-6} \times 2^{-6}$ .

Therefore, the solution to the problem is $9^{-6} \times 2^{-6}$ .

$9^{-6}\times2^{-6}$