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

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: $a+2$

Thus, applying the rule:
$\left(8\times12\right)^{7+x+y - (a+2)}$
Now simplify the expression in the exponent:
$7+x+y - a - 2 = x+y-a+5$

Therefore, the simplified form of the expression is:
$\left(8\times12\right)^{x+y-a+5}$

Comparing this to the given correct answer:
$\left(8\times12\right)^{x+y-a-5}$

It seems there was a mistake in simplification, and re-evaluation is needed to check the calculation for signs.
I couldn't get to the shown answer.