Simplify. Express your answer using positive exponents. \[ 9 g^{5} h \cdot 9 g h^{3} \cdot 6 g h \]

To simplify the expression \( 9 g^{5} h \cdot 9 g h^{3} \cdot 6 g h \), we first multiply the coefficients: \[ 9 \cdot 9 \cdot 6 = 81 \cdot 6 = 486 \] Next, we combine the like bases for \( g \) and \( h \): For \( g \): \[ g^{5} \cdot g \cdot g = g^{5+1+1} = g^{7} \] For \( h \): \[ h \cdot h^{3} \cdot h = h^{1+3+1} = h^{5} \] Now, we can put everything together: \[ 486 g^{7} h^{5} \] Thus, the simplified expression is: \[ \boxed{486 g^{7} h^{5}} \]