Simplify (4×7)^12 ÷ (4×7)^5: Exponent Division Problem

The given expression is $\frac{\left(4\times7\right)^{12}}{\left(4\times7\right)^5}$.
We are asked to simplify this expression using the Power of a Quotient Rule for Exponents.

The Power of a Quotient Rule states:

• When you divide like bases, you subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$.

Applying this rule to the given problem:

1. The base of both the numerator and the denominator is $4 \times 7$.
2. The exponent in the numerator is 12, and the exponent in the denominator is 5.
3. Therefore, subtract the exponents: $12 - 5 = 7$.

The simplified expression becomes:

$\left(4\times7\right)^7$.

The solution to the question is: $\left(4\times7\right)^7$