Answer:
[tex]8\sqrt[3]{(5)}[/tex]
Step-by-step explanation:
We have been given an expression [tex](8\times 320)^{\frac{1}{3}[/tex]. We are asked to find which expression of given expressions is equal to our given expression.
Using exponent property [tex](a)^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex] we can rewrite our given expression as:
[tex]\sqrt[3]{(8\times 320)^1}[/tex]
[tex]\sqrt[3]{(8\times 320)}[/tex]
Rewriting 320 as [tex]64\times 5[/tex] in our given expression we will get,
[tex]\sqrt[3]{(8\times 64\times 5)}[/tex]
[tex]\sqrt[3]{(2^3\times 4^3\times 5)}[/tex]
Pulling our 2 and 4 from cube root we will get,
[tex]2\times 4\sqrt[3]{(5)}[/tex]
[tex]8\sqrt[3]{(5)}[/tex]
Therefore, the expression [tex]8\sqrt[3]{(5)}[/tex] is equal to our given expression and option D is the correct choice.
