For this case we must simplify the following expression:
[tex](\frac {n ^ {\frac {3} {2}}} {n ^ {- \frac {1} {6}}}) ^ {- 3}[/tex]
By definition of power properties we have:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, rewriting the expression:
[tex](n ^ {\frac {3} {2}} * n ^ {\frac {1} {6}}) ^ {- 3} =[/tex]
To multiply powers of the same base, we put the same base and add the exponents:
[tex](n ^ {\frac {3} {2} + \frac {1} {6}}) ^ {- 3} =\\(n ^ {\frac {18 + 2} {12}}) ^ {- 3} =\\(n ^ {\frac {20} {12}}) ^ {- 3} =\\(n ^ {\frac {5} {3}}) ^ {- 3} =[/tex]
We multiply the exponents:
[tex]n ^ {\frac {-15} {3}} =\\n^{-5}[/tex]
ANswer:
Option D
