Question

What is the simplified form of the following expression? Assume a greater-than-or-equal-to 0 and c greater-than-or-equal-to 0

14 (RootIndex 4 StartRoot a Superscript 5 Baseline b squared c Superscript 4 Baseline EndRoot) minus 7 a c (RootIndex 4 StartRoot a b squared EndRoot)
7 a c (RootIndex 4 StartRoot a b squared EndRoot)
7 (RootIndex 4 StartRoot a b squared EndRoot)
Negative 7 (RootIndex 4 StartRoot a b squared EndRoot)
Negative 7 a c (RootIndex 4 StartRoot a b squared EndRoot)

Answer 1

Simplify inside the fourth roots: ∜(a^5 b^2 c^4) = ∜(a^4 c^4 · a b^2) = a c · ∜(a b^2) (since a,c ≥ 0).
So the expression becomes 14ac∜(ab^2) − 7ac∜(ab^2) = 7ac∜(ab^2).

Answer: 7 a c · fourth-root(a b^2).