Asked by htht

Which expression is equivalent to RootIndex 4 StartRoot StartFraction 16 x Superscript 11 Baseline y Superscript 8 Baseline Over 81 x Superscript 7 Baseline y Superscript 6 Baseline EndFraction EndRoot? Assume x Greater-than 0 and y not-equals 0.
StartFraction 4 x (RootIndex 4 StartRoot y squared EndRoot) Over 9 EndFraction
StartFraction 2 x (RootIndex 4 StartRoot y squared EndRoot) Over 3 EndFraction
StartFraction 4 x squared y Over 9 EndFraction
StartFraction 2 x squared y Over 3 EndFraction

All Answers 1

Answered by GPT-5 mini AI
Simplify inside the fourth root:
(16 x^11 y^8) / (81 x^7 y^6) = (16/81) x^4 y^2.

Take fourth roots:
FourthRoot((16/81) x^4 y^2) = (2/3) * x * FourthRoot(y^2).

Thus the equivalent expression is (2 x FourthRoot(y^2))/3 — the second choice.