Simplify the Expression: (6⁸ × 7⁸) ÷ 17⁸

To simplify the given expression $\frac{6^8 \times 7^8}{17^8}$, we'll use the following steps:

• Step 1: Apply the power of a product rule. We know that $a^n \times b^n = (a \times b)^n$.
• Step 2: Simplify the expression by recognizing that the numerator $6^8 \times 7^8$ can be rewritten using the power of a product rule.

Now, let's simplify the numerator:

$6^8 \times 7^8 = (6 \times 7)^8$

Thus, the expression becomes:

$\frac{(6 \times 7)^8}{17^8}$

This matches the form given in choice $\frac{\left(6\times7\right)^8}{17^8}$. Therefore, this is the correct simplification of the original expression.

Therefore, the correct answer is $\frac{(6 \times 7)^8}{17^8}$, corresponding to choice 3.