Question 1019624: 4. Simplify (^4 sqrt 16x^4y^5)(^4 sqrt 243y^7) assuming the variables represent non-negative numbers.
A. 6^4 sqrt 3 xy^3
B. 6xy^3
C. 2xy^4 sqrt y 3^4 ^4 sqrt 3 y^4 sqrt y^3
D. 6x^2Y^2 ^4 sqrt 3
Thank You.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! I am not sure I understand the problem. I will assume this is a fourth root of a square root, since B is not the answer.
The first square root is 4x^2*y^2*sqrt(y),
The second square root is 9y^3*sqrt(3y)
These can be multiplied to get 36x^2*y^6*sqrt (3)
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The fourth root of this must only have a y out front and none of the choices have this.
Furthermore, the constant is a minimum of 2 *fourth root of (3), and no choices have this.
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Just taking the square root of the above gets me 6xy^3 fourth root of 3, which is closest to D, but it is not D.
If there is a fourth root of all of this, y should be cubed, since there are y^12 under the fourth root.
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Therefore, I am misreading the notation of the problem or of the answer choices, and I am unclear as to what is a fourth root and what is a square root here.
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