ghth grade C. 18 Multiply and divide powers: varlable bases 85 P \[ \begin{array}{l}\text { 4)) Simplify. Express your answer using positive exponents. } \\ \frac{5 c^{3}}{5 c+c^{0}}\end{array} \]

To simplify the expression \(\frac{5c^3}{5c + c^0}\), we first need to note that \(c^0\) equals 1. Thus, the denominator simplifies to \(5c + 1\). Now, we rewrite the expression as \(\frac{5c^3}{5c + 1}\). Since \(5c^3\) cannot be simplified further with the \(5c + 1\) in the denominator, the final answer remains \(\frac{5c^3}{5c + 1}\). Remember, you can't divide the terms directly because they aren't like terms! In mathematical terms, this process is a key part of understanding how to handle variables in fractions and simplifying expressions, which is fundamental in algebra. Power rules become especially handy when variables are raised to powers, so keep practicing these concepts!