For this case we must simplify the given expression:
Rewriting we have:
[tex]\sqrt [3] {\frac {2 * 5x ^ 5} {2 * 27x ^ 8}} =\\\sqrt [3] {\frac {5x ^ 5} {27x ^ 8}} =[/tex]
By definition of division of powers of equal base, the same base is placed and the exponents are subtracted:
[tex]\sqrt [3] {\frac {5x ^ {5-8}} {27}} =\\\sqrt [3] {\frac {5x ^ {- 3}} {27}} =\\\sqrt [3] {\frac {5} {27x ^ 3}} =[/tex]
We have to:
[tex]\sqrt [3] {27x ^ 3} = 3x[/tex]
Then, the expression is reduced to:
[tex]\frac {\sqrt [3] {5}} {3x}[/tex]
ANswer:
Option D
