Simplify (9×5)¹² ÷ (5×9)⁶: Power Division Challenge

We begin by analyzing the given expression: $\frac{\left(9\times5\right)^{12}}{\left(5\times9\right)^6}$. Using the property of exponents known as the Power of a Quotient Rule, we can rewrite this expression.
This rule states that $\frac{a^m}{a^n} = a^{m-n}$. Here, both the numerator and the denominator have the same base, $9\times5$ or equivalently $5\times9$, therefore we can apply this rule.

Let's apply the Power of a Quotient Rule:

• Identify the base, which is $9\times5$.

• Subtract the exponent in the denominator from the exponent in the numerator: $12 - 6$.

Thus, the expression simplifies to $\left(9\times5\right)^{12-6}$.

The solution to the question is: $\left(9\times5\right)^{12-6}$.