Calculate (3×8×6×4×2)³: Cubing a Product Expression

Insert the corresponding expression:

$\left(3\times8\times6\times4\times2\right)^3=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:04 According to the laws of exponents, a product that is raised to the power (N)

00:07 Equals a product where each factor is raised to that same power (N)

00:13 This formula is valid regardless of how many factors are in the product

00:24 We will apply this formula to our exercise

00:41 This is the solution

Step-by-Step Solution

To solve this problem, we will use the power of a product rule, which helps distribute the exponent over each factor within the parentheses.

Step 1: Identify the expression. We have $(3 \times 8 \times 6 \times 4 \times 2)^3$ .
Step 2: Apply the power of a product rule. This rule states that if we have a product raised to an exponent, we can distribute the exponent to each factor. Mathematically, $(a \times b \times c \ldots)^n = a^n \times b^n \times c^n \ldots$ .
Step 3: Apply the rule to the expression.

We distribute the exponent 3 to each of the factors inside the parentheses:

$(3 \times 8 \times 6 \times 4 \times 2)^3 = 3^3 \times 8^3 \times 6^3 \times 4^3 \times 2^3$ .

Therefore, the corresponding expression is $3^3 \times 8^3 \times 6^3 \times 4^3 \times 2^3$ .