Divide and simplify if possible

√81x^8/√3x

This step is wrong.

√(9^2 * x^8)/(√3 * √x)
(9x^4 * √x)/(√3 * √x)
It should have been
√(9^2 * x^8)/(√3 * √x)
(9x^4)/(√3 * √x)
(3√3√3 x^3√x√x)(√3√x)
3√3 x^3 √x
or √(27x^7)

You are correct. I apologize for my mistake in simplifying the expression. Following the correct steps:

√(9^2 * x^8)/(√3 * √x)
(9x^4)/(√3 * √x)
(9x^4)/(√(3x))
(3x^4√3x)
√(27x^7)

Thank you for pointing out the error.

√(81x^8)/√(3x)

√(9^2 * x^8)/(√3 * √x)

(9x^4 * √x)/(√3 * √x)

(9x^4)/(√3)

(3x^4√3)