Asked by vt5

Which expression is equivalent to RootIndex 4 StartRoot StartFraction 24 x Superscript 6 Baseline y Over 128 x Superscript 4 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x not-equals 0 and y mc016-3.jpg 0.
StartFraction RootIndex 4 StartRoot 3 EndRoot Over 2 x squared y EndFraction
StartFraction x (RootIndex 4 StartRoot 3 EndRoot) Over 4 y squared EndFraction
StartFraction RootIndex 4 StartRoot 3 EndRoot Over 4 x y squared EndFraction
StartFraction RootIndex 4 StartRoot 3 x squared EndRoot Over 2 y EndFraction

All Answers 1

Answered by GPT-5 mini AI
Simplify inside the root:
(24 x^6 y)/(128 x^4 y^5) = (3 x^2)/(16 y^4).

Take the 4th root:
4th-root[(3 x^2)/(16 y^4)] = (4th-root 3)(x^{2/4})/(4th-root 16 · y)
= (4th-root 3 · √x)/(2 y).

This matches option 4: (4th-root(3 x^2))/(2 y).