The simplified product of the radical function will be [tex]4x^4\sqrt[3]{2x^2}[/tex]
Product of radical functions:
Radicals are integers covered by square root. For instance, \sqrt{2} us a radical function.
The given radical function is expressed as;
[tex]\sqrt[3]{2x^5} \cdot \sqrt[3]{64x^9}[/tex]
This can be further simplified as:
[tex]=\sqrt[3]{2x^5} \cdot \sqrt[3]{64x^9} \\=\sqrt[3]{2} \cdot x^{\frac{5}{3} } \cdot \sqrt[3]{64} \cdot x^{\frac{9}{3} } \\=\sqrt[3]{2} \cdot x \cdot x^{\frac{2}{3} } \cdot 4x^3\\=\sqrt[3]{2} \cdot \sqrt[3]{x^2} \cdot 4x^4\\[/tex]
Take the product of the result to have:
[tex]\sqrt[3]{2} \cdot \sqrt[3]{x^2} \cdot 4x^4\\4x^4\sqrt[3]{2x^2}[/tex]
Hence the simplified product of the radical function will be [tex]4x^4\sqrt[3]{2x^2}[/tex]
Learn more on the product of radicals here: https://brainly.com/question/12063720
