Concept:Simplify the product of powers by adding exponents, then equate the exponent sum to 3.Explanation:The given expression is xa2b−1c−1⋅xb2c−1a−1⋅xc2a−1b−1−x3.Combine exponents: a2b−1c−1+b2c−1a−1+c2a−1b−1.Write each term as a fraction: bca2+cab2+abc2.Common denominator abc gives abca3+b3+c3.For the expression to be zero, we need abca3+b3+c3=3, i.e., a3+b3+c3=3abc.Using the identity a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−ab−bc−ca), the condition holds if a+b+c=0 or a=b=c.Among the options, a+b+c=0 is the required value.Answer:a+b+c=0