What is the simplified form of the fifth root of x to the fourth power times the fifth root of x to the fourth power

I believe the following is your problem (if not do rectify me). If so, then:

⁵√x⁴.⁵√x⁴

1st method:

⁵√x⁴.⁵√x⁴ = x⁴/⁵. x⁴/⁵ = x ⁽⁴/⁵ + x⁴/⁵⁾ = x⁸/⁵ = ⁵√x⁸ = ⁵√ (x⁵. x³) = x. ⁵√x³

2nd method:

⁵√x⁴. ⁵√x⁴ = ⁵√ (x⁴. x⁴) = ⁵√ (x⁴⁺⁴) = ⁵√x⁸ = x.⁵√x³