Question

PLEASE HELP ~ 15 POINTS

Answer 1

For this case we must simplify the following expression:

$(\frac {n ^ {\frac {3} {2}}} {n ^ {- \frac {1} {6}}}) ^ {- 3}$

By definition of power properties we have:

$a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}$

Then, rewriting the expression:

$(n ^ {\frac {3} {2}} * n ^ {\frac {1} {6}}) ^ {- 3} =$

To multiply powers of the same base, we put the same base and add the exponents:

$(n ^ {\frac {3} {2} + \frac {1} {6}}) ^ {- 3} =\\(n ^ {\frac {18 + 2} {12}}) ^ {- 3} =\\(n ^ {\frac {20} {12}}) ^ {- 3} =\\(n ^ {\frac {5} {3}}) ^ {- 3} =$

We multiply the exponents:

$n ^ {\frac {-15} {3}} =\\n^{-5}$

ANswer:

Option D