The mathematical expression in the image is:

$\frac{15^3 - 15^2}{15}$

Step-by-Step Solution:

1. Simplify the numerator: $15^3 - 15^2 = 15^2(15 - 1)$ Factoring $15^2$ out from both terms gives: $15^2 \cdot (15 - 1) = 15^2 \cdot 14$

2. Rewrite the expression: Substituting the factored numerator into the fraction: $\frac{15^2 \cdot 14}{15}$

3. Simplify the fraction: Since $15^2 = 15 \cdot 15$, cancel one $15$ from the numerator and denominator: $\frac{15^2 \cdot 14}{15} = 15 \cdot 14$

4. Calculate the final value: $15 \cdot 14 = 210$

Final Answer:

$\boxed{210}$

Would you like further explanation or a breakdown of any specific step?

Related Questions:

1. How do you factorize higher powers in general?
2. What are common tricks to simplify expressions involving powers?
3. How can this method be applied to different bases (e.g., $x^n - x^{n-1}$)?
4. What happens if you replace 15 with another number, such as 20?
5. How does exponentiation work in modular arithmetic?

Tip:

Always look for common factors in the numerator and denominator to simplify expressions quickly.