2018 · Q3
If x = y^{1/a}, y = z^{1/b} and z = x^{1/c} where x≠1, y≠1, z≠1, then what is the value of abc?
Elementary MathematicsAlgebra
- A-1
- B1
- C0
- D3
Explanation
Raising to powers gives xᵃ = y, yᵇ = z and zᶜ = x (the question asks for the value of abc). Substituting successively: x = zᶜ = (yᵇ)ᶜ = ((xᵃ)ᵇ)ᶜ = xᵃᵇᶜ. Since x ≠ 1, the exponents must match, so abc = 1. The keyed answer is (B).