Question

Which expression is equivalent to RootIndex 4 StartRoot 144 a Superscript 12 Baseline b cubed EndRoot? Assume a greater-than-or-equal-to 0 and b greater-than-or-equal-to 0.
2 a cubed (RootIndex 4 StartRoot 9 b cubed EndRoot)
2 a Superscript 4 Baseline b (RootIndex 4 StartRoot 18 EndRoot)
6 a cubed (RootIndex 4 StartRoot 3 b cubed EndRoot)
12 a Superscript 6 Baseline b (RootIndex 4 StartRoot b EndRoot)

Answer 1

2a^3 * fourth root(9b^3)

Reason: fourth root(144 a^12 b^3) = fourth root(16*9 * a^12 * b^3) = fourth root(16)*fourth root(a^12)*fourth root(9b^3) = 2 * a^3 * fourth root(9b^3) (with a,b ≥ 0 so the real fourth root is valid).