Question

please help and look at the picture

Answer 1

Hello!

The answer is:

D. $8\sqrt[3]{5}$

Why?

To solve the problem, we need to remember the following roots properties:

$a^{\frac{m}{n} }=\sqrt[n]{a^{m} }$

$a\sqrt[n]{b} =\sqrt[n]{a^{n}*b} \\\\\sqrt[n]{ab}=\sqrt[n]{a}*\sqrt[n]{b}$

So, we are given the expression:

$(8.320)^{\frac{1}{3} }$

Then,  writing its equivalent expression, we have:

$\sqrt[3]{8.320}$

Now, simplyfing, we have:

$\sqrt[3]{8.320}=\sqrt[3]{2560}=\sqrt[3]{512*5}\\\\\sqrt[3]{8.320}=\sqrt[3]{512*5}=\sqrt[3]{8^{3} .5}\\\\\sqrt[3]{8.320}=\sqrt[3]{8^{3} .5}=\sqrt[3]{8}*\sqrt[3]{5} \\\\\sqrt[3]{8.320}=\sqrt[3]{8}*\sqrt[3]{5}=8*\sqrt[3]{5}$

Hence, we have that the correct option is:

D. $8\sqrt[3]{5}$

Have a nice day!