$\leftarrow$ Save \& Exit Certify Lesson: 9.2 Simplifying Radicals Question 8 of 10 , Step 1 of 1 $6 / 10$ Correct Simplify the following expression. Assume that each variable is positive. \[ \sqrt[3]{24 x^{5}} \] Answer

Step 1 ：Factorize 24: \(24 = 2^3 \times 3\)

Step 2 ：Simplify \(x^5\)

Step 3 ：Rewrite the expression using prime factorization: \(\sqrt[3]{24 x^{5}} = \sqrt[3]{2^3 \times 3 \times x \times x \times x \times x \times x}\)

Step 4 ：Separate the factors under the cube root: \(\sqrt[3]{2^3} \times \sqrt[3]{3} \times \sqrt[3]{x \times x \times x \times x \times x}\)

Step 5 ：Simplify each cube root separately: \(2 \times \sqrt[3]{3} \times x \times x\)

Step 6 ：Combine like terms: \(2x^2 \sqrt[3]{3}\)