Simplify (9×7)^2x / (7×9)^2y: Comparing Exponential Expressions

To solve the equation, you're required to simplify the expression $\frac{\left(9\times7\right)^{2x}}{\left(7\times9\right)^{2y}}$. This expression contains powers of quotients, and you can apply the properties of exponents to simplify it.

Let's go through the solution step by step:

• Both the numerator and the denominator are raised to some powers. Notice that the base of both the numerator and the denominator is $(9 \times 7)$, since $9 \times 7 = 63$ and $7 \times 9 = 63$.
• Therefore, you can rewrite the expression as $\frac{(63)^{2x}}{(63)^{2y}}$.
• According to the property of exponents, $\frac{a^m}{a^n} = a^{m-n}$, where $a$ is a non-zero number. Apply this rule:
• $\frac{(63)^{2x}}{(63)^{2y}} = (63)^{2x-2y}$

With the simplification completed, you get $\left(63\right)^{2x-2y}$.

Finally, substitute back $63$ for $9 \times 7$, and you can express the result as $\left(9 \times 7\right)^{2x-2y}$.

The solution to the question is: $\left(9\times7\right)^{2x-2y}$.