Simplify (4×7)^(2x)/(4×7)^4: Exponential Expression with Variable Power

We start with the expression: $\frac{\left(4\times7\right)^{2x}}{\left(4\times7\right)^4}$.

According to the Power of a Quotient Rule for Exponents, which states that $\frac{a^m}{a^n} = a^{m-n}$, we can simplify the expression by subtracting the exponents.

The base here is $4 \times 7$, and it is common in both the numerator and the denominator.

Thus, using the exponent rule, we have:

• Exponent in the numerator: $2x$
• Exponent in the denominator: $4$

Now, apply the rule:

$\frac{\left(4\times7\right)^{2x}}{\left(4\times7\right)^4} = \left(4\times7\right)^{2x-4}$

The solution to the question is: $\left(4\times7\right)^{2x-4}$.