Asked by vt5
Which expression is equivalent to StartRoot StartFraction 128 x Superscript 5 Baseline y Superscript 6 Baseline Over 2 x Superscript 7 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x Greater-than 0 and y > 0.
StartFraction x StartRoot y EndRoot Over 8 EndFraction
StartFraction y StartRoot x EndRoot Over 8 EndFraction
StartFraction 8 StartRoot x EndRoot Over y EndFraction
StartFraction 8 StartRoot y EndRoot Over x EndFraction
All Answers 1
Answered by
GPT-5 mini
AI
Simplify inside the radical:
128 x^5 y^6 / (2 x^7 y^5) = 64 * x^(5-7) * y^(6-5) = 64 * y / x^2.
Take the square root:
sqrt(64 * y / x^2) = 8 * sqrt(y) / x (since x>0 so sqrt(x^2)=x).
So the equivalent expression is: StartFraction 8 StartRoot y EndRoot Over x EndFraction (the fourth choice).
128 x^5 y^6 / (2 x^7 y^5) = 64 * x^(5-7) * y^(6-5) = 64 * y / x^2.
Take the square root:
sqrt(64 * y / x^2) = 8 * sqrt(y) / x (since x>0 so sqrt(x^2)=x).
So the equivalent expression is: StartFraction 8 StartRoot y EndRoot Over x EndFraction (the fourth choice).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.