Simplify (15×2)¹⁷ ÷ (2×15)¹³: Power Rules in Action

The given expression is $\frac{\left(15\times2\right)^{17}}{\left(2\times15\right)^{13}}$. To simplify
using the rule of exponents known as the Power of a Quotient Rule, which states

When you divide like bases you subtract the exponents:

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

First, notice that both the numerator and denominator have the base $15 \times 2$. Therefore, we can simplify by subtracting the exponents in the numerator and the denominator:

• Numerator's exponent: 17
• Denominator's exponent: 13

We apply the quotient rule:

$(15 \times 2)^{17-13}$.

As a result, the simplified expression is $(15 \times 2)^4$.
Therefore, the correct answer which represents the expression using the Power of a Quotient Rule is

$\left(15\times2\right)^{17-13}$

because it encapsulates the subtraction of exponents without computing the final exponent 4.

This allows you to keep the expression in its most simplistic exponential form.