The given expression is
[tex]30s^9\colon5t^4\times6t^2[/tex]Notice that the second power is a denominator.
[tex]\frac{30s^9\times6t^2}{5t^4}[/tex]Now, we simplify the numbers and divide the power with a common base.
[tex]\frac{36s^9}{t^2}[/tex]Therefore, the simplified expression is
[tex]\frac{36s^9}{t^2}[/tex]