What is the simplified form of the cube root of x squared times the third root of x squared?

Solution:

The cube root of x squared times the third root of x squared = ∛(x² × ∛x²)

= ∛(x². x^2/3)

Using exponents and powers rule, a^m × aⁿ = a^{m + n}

= ∛(x^8/3)

= (x^8/3)^1/3 [(a^m )ⁿ = a^mn]

= x^8/9

∛(x² × ∛x²) = x^8/9

What is the simplified form of the cube root of x squared times the third root of x squared?

Summary:

The simplified form of the cube root of x squared times the third root of x squared is x^8/9.