SOLUTION: Hi I have a Question! (x^(3a))/(sqrt(x^16a)) The think the answer is x^(-5a) But I do not know how to get that. thanks!

Algebra ->  Radicals -> SOLUTION: Hi I have a Question! (x^(3a))/(sqrt(x^16a)) The think the answer is x^(-5a) But I do not know how to get that. thanks!      Log On


   

Question 604733: Hi I have a Question!
(x^(3a))/(sqrt(x^16a))
The think the answer is x^(-5a)
But I do not know how to get that.
thanks!
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(x^(3a))/(squareroot(x^(16a)))
-------------------
(x^(3a))/(x^8a)
----
= 1/x^(5a)
==============
Cheers,
Stan H.

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
I think that you intended for the exponent in the denominator to be 16a rather than the way you wrote it. In other words you meant:
.
%28x%5E%283a%29%29%2Fsqrt%28x%5E%2816a%29%29+
.
This being the case, then the next step would be to replace the square root radical with the exponent 1/2, which converts the problem to:
.
%28x%5E%283a%29%29%2F%28x%5E%2816a%29%29%5E%281%2F2%29+
.
Following the power rule for exponents in the term in the denominator we can multiply the exponent (1/2) times the exponent (16a) to get an answer of 8a. The problem can therefore be rewritten as:
.
%28x%5E%283a%29%29%2Fx%5E%288a%29%29+
.
Then, since the base for the exponential terms is x in both the numerator and the denominator, we can divide by raising the base to the difference between the two exponents as follows:
.
x%5E%283a-8a%29
.
Subtracting the exponents results in the answer you thought it was, namely:
.
x%5E%28-5a%29
.
I hope that my interpretation of the problem you wanted help with is correct. If not, please post it again and one of the tutors will likely respond.
.