1. The problem is to simplify the expression $14) -\sqrt{81c^{48}d^{64}}$. 2. First, note that the square root of a product is the product of the square roots: $$\sqrt{81c^{48}d^{64}} = \sqrt{81} \times \sqrt{c^{48}} \times \sqrt{d^{64}}.$$ 3. Calculate each square root separately: - $\sqrt{81} = 9$ because $9^2 = 81$. - $\sqrt{c^{48}} = c^{\frac{48}{2}} = c^{24}$ by the rule $\sqrt{x^n} = x^{\frac{n}{2}}$. - $\sqrt{d^{64}} = d^{\frac{64}{2}} = d^{32}$. 4. Multiply these results together: $$9 \times c^{24} \times d^{32} = 9c^{24}d^{32}.$$ 5. The original expression is $14) - \sqrt{81c^{48}d^{64}}$, which means $14 - 9c^{24}d^{32}$. 6. Therefore, the simplified expression is $$14 - 9c^{24}d^{32}.$$