Solve (2×7×3)^(-3): Negative Exponent Expression Problem

Question

Insert the corresponding expression:

$\left(2\times7\times3\right)^{-3}=$

00:00 Simplify the following problem

00:03 In order to open parentheses with a multiplication operation and an outside exponent

00:09 We'll raise each factor to the power

00:15 We'll apply this formula to our exercise

00:23 This is the solution

To solve the expression $(2 \times 7 \times 3)^{-3}$ , let's proceed with the following steps:

Step 1: Recognize that we have a product inside the parentheses, $2 \times 7 \times 3$ , which is raised to the power of $-3$ .

Step 2: Apply the power of a product rule, which states that $(a \times b \times c)^n = a^n \times b^n \times c^n$ . This gives us:

$(2 \times 7 \times 3)^{-3} = 2^{-3} \times 7^{-3} \times 3^{-3}$

Therefore, applying the exponent rule, we have:

$2^{-3} \times 7^{-3} \times 3^{-3}$

$2^{-3}\times7^{-3}\times3^{-3}$