Question

PLEASE HELP ~ 15 POINTS

Which expression is equivalent to (n^3/2 ÷ n^-1/6)
A. n^27
B. n^-27
C. n^-4
D. n^-5

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