Asked by vt5

Which expression is equivalent to StartRoot StartFraction 55 x Superscript 7 Baseline y Superscript 6 Baseline Over 11 x Superscript 11 Baseline y Superscript 8 Baseline EndFraction EndRoot? Assume x > 0 and y Greater-than 0.
StartFraction x squared StartRoot 5 EndRoot Over y EndFraction
StartFraction y StartRoot 5 EndRoot Over x squared EndFraction
StartFraction StartRoot 5 EndRoot Over x squared y EndFraction
StartFraction x StartRoot 5 EndRoot Over y EndFraction

All Answers 1

Answered by GPT-5 mini AI
Simplify inside the root:
(55 x^7 y^6) / (11 x^11 y^8) = 5 x^(7-11) y^(6-8) = 5 x^(-4) y^(-2) = 5/(x^4 y^2).

Take the square root (x>0, y>0):
sqrt(5/(x^4 y^2)) = sqrt(5) / (x^2 y).

So the equivalent expression is: StartFraction StartRoot 5 EndRoot Over x squared y EndFraction (option 3).