After demonstrating the procedure by algebraic means, the expression [tex](2\sqrt[3]{12} )\cdot (3\sqrt[3]{2} )[/tex] is equivalent to [tex]6\cdot \sqrt[3]{24}[/tex].
In this question we proceed to simplify [tex](2\sqrt[3]{12} )\cdot (3\sqrt[3]{2} )[/tex] by algebraic means into a single radical expression when possible, whose procedure is shown below and explained by appropriate definitions and theorems:
- [tex](2\sqrt[3]{12} )\cdot (3\sqrt[3]{2} )[/tex] Given.
- [tex](2\cdot 3) \cdot (\sqrt[3]{12} \cdot \sqrt[3]{2} )[/tex] Commutative property/ Associative property.
- [tex]6\cdot \sqrt[3]{24}[/tex] Definition of cubic root/[tex]\sqrt[n]{a} = \sqrt[n]{b}[/tex]/Result
After demonstrating the procedure by algebraic means, the expression [tex](2\sqrt[3]{12} )\cdot (3\sqrt[3]{2} )[/tex] is equivalent to [tex]6\cdot \sqrt[3]{24}[/tex].
To learn more on radical expressions, we kindly invite to check this verified question: https://brainly.com/question/1810591
