Simplify the expression shown by collecting like surds where possible. \[ \sqrt[3]{-56}+\sqrt[3]{-189} \] INSTRUCTIONS: 1. Do not use a calculator. 2. Write your answer with an exponent. Type ?^(1/2) for a square root or ?^(1/3) for a cube root. Answer: \( \sqrt[3]{-56}+\sqrt[3]{-189}= \)

To simplify the expression \( \sqrt[3]{-56} + \sqrt[3]{-189} \), we start by breaking down each term into prime factors. First, we simplify \( \sqrt[3]{-56} \): \[ -56 = -1 \times 2^3 \times 7 \] Thus, \[ \sqrt[3]{-56} = \sqrt[3]{-1} \times \sqrt[3]{2^3} \times \sqrt[3]{7} = -1 \times 2 \times \sqrt[3]{7} = -2 \sqrt[3]{7} \] Now, for \( \sqrt[3]{-189} \): \[ -189 = -1 \times 3^3 \times 7 \] So, \[ \sqrt[3]{-189} = \sqrt[3]{-1} \times \sqrt[3]{3^3} \times \sqrt[3]{7} = -1 \times 3 \times \sqrt[3]{7} = -3 \sqrt[3]{7} \] Now, we can combine the two simplified surds: \[ -2 \sqrt[3]{7} - 3 \sqrt[3]{7} = (-2 - 3) \sqrt[3]{7} = -5 \sqrt[3]{7} \] Putting it all together, we have: \[ \sqrt[3]{-56} + \sqrt[3]{-189} = -5 \sqrt[3]{7} \] In exponent form, we can write the cube root: Answer: \( -5 \cdot 7^{(1/3)} \)