{
    "problem": "Simplify $\\sqrt[3]{1+8} \\cdot \\sqrt[3]{1+\\sqrt[3]{8}}$.",
    "level": "Level 2",
    "type": "Algebra",
    "solution": "The first cube root becomes $\\sqrt[3]{9}$. $\\sqrt[3]{8}=2$, so the second cube root becomes $\\sqrt[3]{3}$. Multiplying these gives $\\sqrt[3]{27} = \\boxed{3}$."
}