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!

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) (Show Source): You can put this solution on YOUR website!
(x^(3a))/(squareroot(x^(16a)))
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(x^(3a))/(x^8a)
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= 1/x^(5a)
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Cheers,
Stan H.
Answer by bucky(2189) (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:
.

.
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:
.

.
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:
.

.
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:
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Subtracting the exponents results in the answer you thought it was, namely:
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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.
.
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