a. \( \frac{x^{3} \cdot x^{8}}{x^{2}} \)

To simplify the expression \( \frac{x^{3} \cdot x^{8}}{x^{2}} \), first combine the terms in the numerator. According to the property of exponents, when multiplying like bases, you add the exponents: \( x^{3} \cdot x^{8} = x^{3 + 8} = x^{11} \). Now the expression looks like \( \frac{x^{11}}{x^{2}} \). When dividing like bases, you subtract the exponents: \( x^{11 - 2} = x^{9} \). So, the simplified form is \( x^{9} \). Remember, when performing operations with exponents, it's all about keeping track of those little numbers! Missing an exponent can send you on a whole different math trajectory. Double-check your work and enjoy the beauty of exponent rules—they make life much simpler!