Which of the following is equal to the expression below \( (8 \cdot 320)^{\frac{1}{3}} \) A. 40 B. \( 8 \sqrt[3]{5} \) C. 30 D. \( 10 \sqrt[3]{5} \)

To determine which option is equal to the expression \( (8 \cdot 320)^{\frac{1}{3}} \), let's simplify the expression step by step. 1. **Multiply the values inside the parentheses:** \[ 8 \cdot 320 = 2560 \] 2. **Express 2560 in terms of its prime factors:** \[ 2560 = 2^9 \cdot 5 \] 3. **Apply the cube root to the prime factorization:** \[ (2^9 \cdot 5)^{\frac{1}{3}} = 2^{3} \cdot 5^{\frac{1}{3}} = 8 \cdot \sqrt[3]{5} \] So, the simplified form of \( (8 \cdot 320)^{\frac{1}{3}} \) is \( 8 \sqrt[3]{5} \). **Answer:** **B. \( 8 \sqrt[3]{5} \)**