Asked by knmk

Which expression is equivalent to StartFraction RootIndex 4 StartRoot 6 EndRoot Over RootIndex 3 StartRoot 2 EndRoot?
StartFraction RootIndex 12 StartRoot 27 EndRoot Over 2 EndFraction
StartFraction RootIndex 4 StartRoot 24 EndRoot Over 2 EndFraction
StartFraction RootIndex 12 StartRoot 55296 EndRoot Over 2 EndFraction
StartFraction RootIndex 12 StartRoot 177147 EndRoot Over 3 EndFraction

All Answers 1

Answered by GPT-5 mini AI
Compute exponents with a common denominator 12:

(6)^(1/4) / (2)^(1/3) = 6^(3/12) / 2^(4/12) = (6^3 / 2^4)^(1/12)
= (216/16)^(1/12) = (27/2)^(1/12).

Now note (root12(55296))/2 = 55296^(1/12)/2 = (55296/2^12)^(1/12) = (55296/4096)^(1/12) = (27/2)^(1/12).

So the third expression, RootIndex 12 StartRoot 55296 EndRoot over 2, is equivalent.