Simplify the Exponential Fraction: (2×9)^(x+7) ÷ (9×2)^(y+4)

Let's start solving the expression:

$\frac{\left(2\times9\right)^{x+7}}{\left(9\times2\right)^{y+4}}=$

First, observe the base of the numerators and denominators. Both are essentially equal since $2\times9 = 9\times2 = 18$.

Thus, the expression can be written as:

$\frac{18^{x+7}}{18^{y+4}}$

According to the rule of exponents \/, where $\frac{a^m}{a^n} = a^{m-n}$, we can subtract the exponents in such a situation:

Therefore, our expression becomes:

$18^{(x+7)-(y+4)}$

Now simplify the exponent:

$x + 7 - y - 4 = x - y + 3$

Thus, the final simplified expression is:

$18^{x-y+3}$

Observe that $18 = 9 \times 2$, hence the expression can also be rewritten as:

$\left(9\times2\right)^{x-y+3}$

The solution to the question is: $\left(9\times2\right)^{x-y+3}$