Question

Which expression is equivalent to RootIndex 3 StartRoot 64 a Superscript 6 Baseline b Superscript 7 Baseline c Superscript 9 Baseline EndRoot?
2 a b c squared (RootIndex 3 StartRoot 4 a squared b cubed c EndRoot)
4 a squared b squared c cubed (RootIndex 3 StartRoot b EndRoot)
8 a cubed b cubed c Superscript 4 Baseline (RootIndex 3 StartRoot b c EndRoot)
8 a squared b squared c cubed (RootIndex 3 StartRoot b EndRoot)

Answer 1

4 a^2 b^2 c^3 (RootIndex 3 StartRoot b EndRoot)

Reason: 64 = 4^3, a^6 = (a^2)^3, b^7 = (b^2)^3·b, c^9 = (c^3)^3, so
∛(64 a^6 b^7 c^9) = 4 a^2 b^2 c^3 ∛b.