Simplify (8×7)^15 Divided by (8×7)^3: Power Division Problem

We are given the expression: $\frac{\left(8\times7\right)^{15}}{\left(8\times7\right)^3}$

To solve this, we can use the Power of a Quotient Rule for Exponents. This rule states that for any non-zero numbers $a$ and $b$, and any integers $m$ and $n$, the expression:

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

can be simplified by subtracting the exponent in the denominator from the exponent in the numerator.

Using the Power of a Quotient Rule, let's apply it to our expression:

Given: $\frac{\left(8\times7\right)^{15}}{\left(8\times7\right)^3}$

According to the rule: $\left(8\times7\right)^{15-3}$

So, the simplified expression is: $\left(8\times7\right)^{12}$

Thus, the correct simplified expression is: $\left(8\times7\right)^{15-3}$