12. \( -6\left(\frac{2}{3} p^{8}\right)^{3} \)

Let's explore how to simplify the expression \( -6\left(\frac{2}{3} p^{8}\right)^{3} \) in an engaging way! First, when you raise a fraction to a power, you raise both the numerator and denominator. So, \(\left(\frac{2}{3}\right)^{3} = \frac{2^{3}}{3^{3}} = \frac{8}{27}\). Next, for the term \(p^{8}\), you just raise it to the third power: \(p^{8 \cdot 3} = p^{24}\). Thus, putting everything together, your expression becomes: \(-6 \cdot \frac{8}{27} \cdot p^{24} = -\frac{48}{27} p^{24}\). You can simplify \(-\frac{48}{27}\) to \(-\frac{16}{9}\). So, the final result is: \(-\frac{16}{9} p^{24}\). Now you have a fun, vibrant expression! Keep on solving and simplifying more! For more practice, try raising other numbers and variables to the third power! You can create funky combinations and see what expressions come to life. Maybe even try it with real-world applications like physics or chemistry equations — it could make those principles even more exciting. Keep that math momentum going!