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

Insert the corresponding expression:

$\frac{\left(15\times2\right)^{17}}{\left(2\times15\right)^{13}}=$

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