Simplify the Expression: (3×14)^(a+1) ÷ (3×14)^2

We're given the expression:

$\frac{\left(3\times14\right)^{a+1}}{\left(3\times14\right)^2}$

The problem requires us to simplify this expression using the power of a quotient rule for exponents. This rule states that:

• $\frac{x^m}{x^n} = x^{m-n}$

In our case, we identify:

• $x = 3\times14$
• $m = a+1$
• $n = 2$

Applying the power of a quotient rule, we get:

$\frac{\left(3\times14\right)^{a+1}}{\left(3\times14\right)^2} = \left(3\times14\right)^{a+1-2}$

Therefore, the solution to the question is:

$\left(3\times14\right)^{a-1}$