1. **State the problem:** Simplify the expression $\sqrt{16x^4t^6}$. 2. **Recall the formula:** The square root of a product is the product of the square roots: $$\sqrt{a b} = \sqrt{a} \times \sqrt{b}$$. 3. **Apply the formula:** $$\sqrt{16x^4t^6} = \sqrt{16} \times \sqrt{x^4} \times \sqrt{t^6}$$ 4. **Simplify each square root:** - $\sqrt{16} = 4$ because $4^2 = 16$. - $\sqrt{x^4} = x^{\frac{4}{2}} = x^2$. - $\sqrt{t^6} = t^{\frac{6}{2}} = t^3$. 5. **Combine the simplified parts:** $$4 \times x^2 \times t^3 = 4x^2t^3$$ **Final answer:** $$\boxed{4x^2t^3}$$