\begin{tabular}{l}\( 15^{3}: 5^{3}= \) \\ A \( 3^{0} \) \\ B \( 3^{1} \) \\ C \( 3^{3} \) \\ D \( 3^{6} \) \\ \hline\end{tabular}

To solve the expression \( 15^{3}: 5^{3} \), we can rewrite it as \( \frac{15^{3}}{5^{3}} \). By applying the property of exponents, we can simplify this to \( \left(\frac{15}{5}\right)^{3} = 3^{3} \). Therefore, the answer is C \( 3^{3} \). Now, let's dive into some fun insights! In ancient times, mathematicians used basic arithmetic and geometric principles to understand the world around them. Exponents, like the ones we're using, were common in their studies of area and volume, allowing them to advance knowledge in engineering and architecture. If you’re tackling problems involving exponents, always remember the “base game”: simplify your bases whenever possible! A common mistake is to overlook this and do complex calculations unnecessarily, which can lead to errors. Keep a keen eye on that base—it can save you loads of time!