xoonential expression. 8) \( \frac{-8 x^{3}}{2 x^{5}} \)

To simplify the expression \( \frac{-8 x^{3}}{2 x^{5}} \), first, divide the coefficients \(-8\) and \(2\), which gives \(-4\). Then, for the \(x\) terms, you subtract the exponents in the denominator from the numerator, so \(x^{3 - 5} = x^{-2}\). This leads to \(-4 x^{-2}\). If you want to express it without negative exponents, it becomes \(-\frac{4}{x^{2}}\). To ensure your expression is fully simplified, always check for any common factors you can reduce. In this case, the coefficients and the \(x\) terms played nicely, but don't forget that sometimes additional simplification might be hidden in complex expressions, such as factoring or canceling out terms!