To simplify the expression $\frac{x^7 \cdot x^8}{x}$, let's follow the rules of exponents:

1. Multiply the exponents when multiplying terms with the same base:

   $x^7 \cdot x^8 = x^{7+8} = x^{15}$

2. Divide the exponents when dividing terms with the same base:

   $\frac{x^{15}}{x} = x^{15-1} = x^{14}$

So, the simplified expression is:

$\frac{x^7 \cdot x^8}{x} = x^{14}$

Would you like a detailed explanation of each step? Here are some related questions you might find helpful:

1. How do you simplify expressions with multiple variables and exponents?
2. What are the basic rules of exponents?
3. How do you handle negative exponents in a fraction?
4. How do you simplify expressions involving both multiplication and division of exponents?
5. What are some common mistakes when simplifying exponents?

Tip: When working with exponents, always remember the basic rules: multiply exponents when multiplying like bases, and subtract exponents when dividing like bases!