1. The problem is to understand how to get the expression $5 \times 10^{8} q^{2}$. 2. This expression is a product of three parts: the number 5, the power of ten $10^{8}$, and the variable $q$ squared, $q^{2}$. 3. The number 5 is a coefficient, which means it multiplies the rest of the expression. 4. The term $10^{8}$ means 10 raised to the power of 8, which equals 100,000,000. 5. The variable $q^{2}$ means $q$ multiplied by itself, or $q \times q$. 6. When you multiply these parts together, you get $5 \times 10^{8} \times q^{2}$. 7. This is a standard way to write very large numbers multiplied by variables in algebra and science, especially in scientific notation. 8. So, $5 \times 10^{8} q^{2}$ means 5 times 100,000,000 times $q$ squared.