Which expression is equivalent to 4th root of 144 A to the 12th power b cubed ? Assume A is greater than or equal to 0 and b is greater than or equal to 0

Factor the radicand into perfect fourth powers and what remains: 144A^12b^3 = 16·(A^3)^4·9b^3. Taking the fourth root of the perfect fourth powers gives 2A^3, leaving the fourth root of 9b^3. Thus the equivalent expression is 2A^3 times the fourth root of 9b^3, choice A.

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