Calculate (9×6×8)^5: Fifth Power of a Product Expression

Choose the expression that corresponds to the following:

$\left(9\times6\times8\right)^5=$

To solve the given problem, we'll utilize the power of a product rule. This rule states that:

$(a \times b \times c)^n = a^n \times b^n \times c^n$

Let's apply this rule to the expression $(9 \times 6 \times 8)^5$:

$(9 \times 6 \times 8)^5 = 9^5 \times 6^5 \times 8^5$

It's important to note that when using this rule, the order of terms under multiplication does not affect the result due to the commutative property of multiplication. Thus, any permutation of the factors yields the same mathematical value. Hence, the expression can also be written as:

• $8^5 \times 6^5 \times 9^5$
• $8^5 \times 9^5 \times 6^5$
• $9^5 \times 8^5 \times 6^5$

Upon reviewing the answer choices, each choice represents a valid permutation of $9^5 \times 6^5 \times 8^5$.

This leads us to conclude that all given options are correct, including the explicit choice stating this fact.

Therefore, the solution to the problem is: All answers are correct.