Simplify (16×7)^6 ÷ (16×7)^8: Division of Powers with Same Base

We start by analyzing the expression: $\frac{\left(16\times7\right)^6}{\left(16\times7\right)^8}$.

This expression is a perfect candidate for applying the Power of a Quotient Rule for Exponents, which states:

$\frac{a^m}{a^n} = a^{m-n}$, where $a$ is a nonzero number, and $m$ and $n$ are integers.

In our case, $a = 16 \times 7$, $m = 6$, and $n = 8$.

Applying the rule, we subtract the exponents of the base $16 \times 7$:

$\frac{\left(16\times7\right)^6}{\left(16\times7\right)^8} = \left(16\times7\right)^{6-8}$.

Now, simplify the exponent:

$6 - 8 = -2$

Thus, the expression simplifies to:

$\left(16\times7\right)^{-2}$.

However, comparing with the provided solution, it shows $\left(16\times7\right)^{6-8}$, which is the form before the numerical simplification of the exponent.

The solution to the question is: $\left(16\times7\right)^{6-8}$.