SOLUTION: Write the radical expression (8)/(root(7,x^15)) in exponential form. (a) 8x^-7/15 (b) 8x^15/7 (c) 8x^-15/7 (d) 8x^7/15

Algebra ->  Radicals -> SOLUTION: Write the radical expression (8)/(root(7,x^15)) in exponential form. (a) 8x^-7/15 (b) 8x^15/7 (c) 8x^-15/7 (d) 8x^7/15      Log On


   

Question 929860: Write the radical expression (8)/(root(7,x^15)) in exponential form.
(a) 8x^-7/15
(b) 8x^15/7
(c) 8x^-15/7
(d) 8x^7/15
Found 2 solutions by MathLover1, ewatrrr:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

8%2F%28root%287%2Cx%5E15%29%29
8%2F%28x%5E%2815%2F7%29%29
8x%5E%28-15%2F7%29
so, answer is (c) 8x%5E%28-15%2F7%29

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
8%2Froot%287%2Cx%5E15%29 = 8/x^(15/7) = 8x^(-15/7)
.......
a%5E0+=+1
x%5Em%2Fx%5En=x%5E%28m-n%29
%28+x%5Em+%29%28+x%5En+%29+=+x%5E%28+m+%2B+n+%29
%28a%5Ep%29%5Eq+=+a%5E%28p%2Aq%29
%28xy%29%5En+=+x%5En%2Ay%5En
root%28a%2Cp%29%2Aroot%28a%2Cq%29+=+root%28a%2Cp%2Aq%29
root++%28n%2C+%28x%2Fy%29%29+=+root%28n%2Cx%29%2Froot%28n%2Cy%29
x^(1/n) = root%28n%2Cx%29
root%28n%2Cx%5Em%29%29 = x^(m/n) *****