Hello!
The answer is:
D. [tex]8\sqrt[3]{5}[/tex]
Why?
To solve the problem, we need to remember the following roots properties:
[tex]a^{\frac{m}{n} }=\sqrt[n]{a^{m} }[/tex]
[tex]a\sqrt[n]{b} =\sqrt[n]{a^{n}*b} \\\\\sqrt[n]{ab}=\sqrt[n]{a}*\sqrt[n]{b}[/tex]
So, we are given the expression:
[tex](8.320)^{\frac{1}{3} }[/tex]
Then, writing its equivalent expression, we have:
[tex]\sqrt[3]{8.320}[/tex]
Now, simplyfing, we have:
[tex]\sqrt[3]{8.320}=\sqrt[3]{2560}=\sqrt[3]{512*5}\\\\\sqrt[3]{8.320}=\sqrt[3]{512*5}=\sqrt[3]{8^{3} .5}\\\\\sqrt[3]{8.320}=\sqrt[3]{8^{3} .5}=\sqrt[3]{8}*\sqrt[3]{5} \\\\\sqrt[3]{8.320}=\sqrt[3]{8}*\sqrt[3]{5}=8*\sqrt[3]{5}[/tex]
Hence, we have that the correct option is:
D. [tex]8\sqrt[3]{5}[/tex]
Have a nice day!
