Simplify the radicals and collect the like terms
6√54x^5 / 2√2x
To simplify the radicals, we can simplify the numbers beneath the square roots.
√54 = √(2*3*3*3) = 3√2
√2x = √(2*x) = √2 * √x = √2x
Now we can rewrite the expression:
6√54x^5 / 2√2x = (6 * 3√2 * x^5) / (2 * √2 * x)
Next, we can cancel out the like terms:
(6/2)(3√2 * x^5) / (√2 * x) = 3 * 3√2 * x^5 / √2 * x
The x in the numerator and the denominator can be canceled out:
= 3 * 3√2 * x^4
= 9x^4√2
Therefore, the simplified expression is 9x^4√2.