How do you simplify the cube root of x squared times the square root of x?

Personally I prefer to convert roots to fractional powers for this kind of problem. cube root of x squared is x2/3, and square root of x is x1/2. Adding the exponents, you get x2/3 times x1/2 = x7/6, that is, the sixth root of x to the seventh power - where it doesn't matter whether you take the sixth root first, or raise to the sevents power first.

Alternatively, you can convert all roots to sixth roots, and multiply - and of course, get the same result.