Sure, let's break down the solution step-by-step for each term:
1. First term: [tex]\(\sqrt[3]{4} \cdot \sqrt{3}\)[/tex]
[tex]\(\sqrt[3]{4}\)[/tex] is the cube root of 4.
[tex]\(\sqrt{3}\)[/tex] is the square root of 3.
When we multiply these values, we get approximately [tex]\(2.749459273997205\)[/tex].
2. Second term: [tex]\(2(\sqrt[6]{9})\)[/tex]
[tex]\(\sqrt[6]{9}\)[/tex] is the sixth root of 9.
When we multiply [tex]\(\sqrt[6]{9}\)[/tex] by 2, we get approximately [tex]\(2.8844991406148166\)[/tex].
3. Third term: [tex]\(\sqrt[6]{12}\)[/tex]
[tex]\(\sqrt[6]{12}\)[/tex] is the sixth root of 12.
This value is approximately [tex]\(1.5130857494229015\)[/tex].
4. Fourth term: [tex]\(\sqrt[6]{432}\)[/tex]
[tex]\(\sqrt[6]{432}\)[/tex] is the sixth root of 432.
This value is approximately [tex]\(2.7494592739972052\)[/tex].
5. Fifth term: [tex]\(2(\sqrt[6]{3,888})\)[/tex]
[tex]\(\sqrt[6]{3,888}\)[/tex] is the sixth root of 3,888.
When we multiply [tex]\(\sqrt[6]{3,888}\)[/tex] by 2, we get approximately [tex]\(7.930812913000376\)[/tex].
So, the product of these values is:
[tex]\[
(2.749459273997205) \cdot (2.8844991406148166) \cdot (1.5130857494229015) \cdot (2.7494592739972052) \cdot (7.930812913000376)
\][/tex]
You then multiply these values to get the final product of the expression. Each term has been approximated computationally to give you the most accurate result.
