if a+b+c=0 ,then prove that x^b^-1.x^b=1

Question

it is a problem from algebra of 10th standard

Answer 1

x^b⁻¹x^b=x^b⁻¹+b=x^1/b+b=x^(b²+1)/b.

If (b²+1)/b=0 then x^(b²+1)/b=1. However, b²+1≠0 for any b. This also applies if x is replaced by a or c; or if b is replaced by a or c.

Note that neither a nor c appears in the proposed equality. The question has therefore been wrongly or misleadingly stated or is incomplete.

One possible simple proposition would be x^ax^bx^c=1, because x^a+b+c=x⁰=1.