7. \( \frac{6 a^{8}}{2 a^{3}} \)

To simplify the expression \( \frac{6 a^{8}}{2 a^{3}} \), start by dividing the coefficients and then apply the rules of exponents. The coefficient \( \frac{6}{2} = 3 \). For the exponents, use the property \( \frac{a^m}{a^n} = a^{m-n} \). Therefore, \( a^{8-3} = a^{5} \). Putting it all together, you get \( 3a^{5} \). Next time you encounter rational expressions, remember that breaking them down step by step can make even the trickiest problems feel more manageable. Keeping an eye on both numerical coefficients and variable powers is your secret sauce for mastering simplifications!