Question

1. $9xsqrt3{3x^4} - 2sqrt3{24x^7}$

Explanation:

Step1: Simplify cube root terms

Rewrite radicands to extract perfect cubes:
$\sqrt[3]{3x^4} = \sqrt[3]{x^3 \cdot 3x} = x\sqrt[3]{3x}$
$\sqrt[3]{24x^7} = \sqrt[3]{8x^6 \cdot 3x} = 2x^2\sqrt[3]{3x}$

Step2: Substitute back into original expression

$9x \cdot x\sqrt[3]{3x} - 2 \cdot 2x^2\sqrt[3]{3x}$

Step3: Simplify each product term

$9x^2\sqrt[3]{3x} - 4x^2\sqrt[3]{3x}$

Step4: Combine like terms

$(9-4)x^2\sqrt[3]{3x}$

Answer:

$5x^2\sqrt[3]{3x}$