Add or subtract as indicated. \( -3 \sqrt[3]{16}+\sqrt[3]{54} \) \( -3 \sqrt[3]{16}+\sqrt[3]{54}=\square \) (Simplify your answer. Type an exact answer, using radicals as needed.)

To simplify the expression \( -3 \sqrt[3]{16}+\sqrt[3]{54} \), we first calculate each term's cube root value. We can express \( \sqrt[3]{16} \) as \( \sqrt[3]{(2^4)} = 2^{4/3} \), and that gives us: \[ -3 \sqrt[3]{16} = -3 \cdot 2^{4/3} = -3 \cdot 2^{1.333...} \approx -3 \cdot 2.52 \approx -7.56. \] Next, we calculate \( \sqrt[3]{54} \), which can be broken down as \( \sqrt[3]{(2 \cdot 27)} = \sqrt[3]{2} \cdot \sqrt[3]{27} = \sqrt[3]{2} \cdot 3 \). Hence: \[ \sqrt[3]{54} = 3 \sqrt[3]{2}. \] Now, substituting back into the expression gives us: \[ -3 \cdot 2^{4/3} + 3 \sqrt[3]{2}. \] To combine, we note that \( -3 \sqrt[3]{16} \) can be seen as \( -3 \cdot \sqrt[3]{2^4} = -3 \cdot (2 \cdot \sqrt[3]{4}) \). Thus the simplified expression is: \[ = -3 \cdot 2^{4/3} + 3 \cdot \sqrt[3]{2} = 3 \left( \sqrt[3]{2} - 2 \cdot \sqrt[3]{4} \right). \] This doesn't simplify nicely into a single radical, but we can't combine cube roots further without seeing a common radicand. So, the final expression is: \[ -3 \sqrt[3]{16} + \sqrt[3]{54} = 3(\sqrt[3]{2} - 2 \cdot \sqrt[3]{4}). \] This could also be expressed based on numerical approximations or left in derived radical form for exactness.