Rewrite \( \sqrt[3]{192} \) in simplest form

To simplify \( \sqrt[3]{192} \), we start by factoring 192 into its prime factors. The prime factorization of 192 is \( 2^6 \times 3^1 \). Rewrite the cube root as: \[ \sqrt[3]{192} = \sqrt[3]{2^6 \times 3^1} = \sqrt[3]{(2^6)} \times \sqrt[3]{(3^1)}. \] Now, simplify each term. The cube root of \( 2^6 \) is \( 2^{6/3} = 2^2 = 4 \), and the cube root of \( 3^1 \) is \( 3^{1/3} \). Therefore, we have: \[ \sqrt[3]{192} = 4 \times \sqrt[3]{3}. \] So, the simplest form of \( \sqrt[3]{192} \) is: \[ 4\sqrt[3]{3}. \]