1. The problem asks for the coefficient in the expression $18^3y^3$. 2. The coefficient is the numerical factor multiplying the variable part of the term. 3. First, calculate $18^3$ which means $18 \times 18 \times 18$. 4. Calculate step-by-step: $18 \times 18 = 324$. 5. Then multiply $324 \times 18 = 5832$. 6. Therefore, the coefficient of the expression $18^3y^3$ is $5832$.