Simplify (8×12)^(7+x+y) ÷ (8×12)^(a+2): Exponential Expression Challenge

Insert the corresponding expression:

$\frac{\left(8\times12\right)^{7+x+y}}{\left(8\times12\right)^{a+2}}=$

We are given the expression: $\frac{\left(8\times12\right)^{7+x+y}}{\left(8\times12\right)^{a+2}}$.
Our goal is to simplify this expression using the properties of exponents, particularly the quotient rule.

The quotient rule for exponents states that $\frac{a^m}{a^n} = a^{m-n}$, where both expressions have the same base.

In the expression $\frac{\left(8\times12\right)^{7+x+y}}{\left(8\times12\right)^{a+2}}$, the base is $8\times12$ and is common for both the numerator and the denominator.

Using the quotient rule, we subtract the exponents:

• Numerator exponent: $7+x+y$
• Denominator exponent: $a+2$