Simplify (9×7)^9 ÷ (9×7)^4: Exponential Division Problem

Insert the corresponding expression:

$\frac{\left(9\times7\right)^9}{\left(9\times7\right)^4}=$

Let's solve the given expression: $\frac{\left(9\times7\right)^9}{\left(9\times7\right)^4}$.

We need to use the Power of a Quotient Rule for exponents. The rule states that:

$\frac{a^m}{a^n} = a^{m-n}$

In our expression, $a = 9 \times 7$, $m = 9$, and $n = 4$.

Applying the rule, we have:

$\frac{\left(9\times7\right)^9}{\left(9\times7\right)^4} = \left(9\times7\right)^{9-4}$

Perform the subtraction in the exponent:

$9 - 4 = 5$

So the expression simplifies to:

$\left(9\times7\right)^5$

Therefore, the expression $\frac{\left(9\times7\right)^9}{\left(9\times7\right)^4}$ simplifies to $\left(9\times7\right)^5$, which is indeed the correct answer.