Calculate (9×7×6×2)^6: Complex Product Exponentiation

Question

Insert the corresponding expression:

$\left(9\times7\times6\times2\right)^6=$

00:00 Simplify the following problem

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

00:09 equals a product where each factor is raised to that same power (N)

00:16 This formula is valid regardless of how many factors are in the product

00:20 We will apply this formula to our exercise

00:25 We will break down the product into each factor separately raised to the power (N)

00:35 This is the solution

Let's solve the problem by using the power of a product rule:

The given expression is $(9 \times 7 \times 6 \times 2)^6$ .
According to the rule $(a \times b \times c)^n = a^n \times b^n \times c^n$ , we need to distribute the power of 6 to each element in the product inside the brackets.
Apply the rule: $(9 \times 7 \times 6 \times 2)^6 = 9^6 \times 7^6 \times 6^6 \times 2^6$ .

Therefore, the expression simplifies to $9^6 \times 7^6 \times 6^6 \times 2^6$ .

$9^6\times7^6\times6^6\times2^6$