2. Simplify \( 6 h^{2} \div 2 h^{-2}-h \times h^{3}-\frac{4}{h^{-4}} \)

To simplify the expression \( 6 h^{2} \div 2 h^{-2}-h \times h^{3}-\frac{4}{h^{-4}} \), let's break it down step by step. 1. **Simplifying the first term**: \[ 6 h^{2} \div 2 h^{-2} = 6 h^{2} \times \frac{1}{2 h^{-2}} = \frac{6}{2} h^{2} \cdot h^{2} = 3 h^{2 + 2} = 3 h^{4} \] 2. **Simplifying the second term**: \[ -h \times h^{3} = -h^{1 + 3} = -h^{4} \] 3. **Simplifying the third term**: \[ -\frac{4}{h^{-4}} = -4 h^{4} \quad (\text{because } \frac{1}{h^{-4}} = h^{4}) \] Now, combine all the simplified terms together: \[ 3 h^{4} - h^{4} - 4 h^{4} = (3 - 1 - 4) h^{4} = -2 h^{4} \] Thus, the simplified expression is: \[ \boxed{-2 h^{4}} \]