Factor the following.
[(5/3x)^(3/2)] - [2/3x] + [(1/3x)^(-1/2)]
To factor the given expression, let's simplify each term and look for common factors.
Term 1: [(5/3x)^(3/2)]
The exponent 3/2 means we need to take the square root of the base raised to the power of 3.
√[(5/3x)^3] = (5/3x)^(3/2)
Term 2: [2/3x]
This term is already simplified and cannot be factorized further.
Term 3: [(1/3x)^(-1/2)]
The negative exponent -1/2 means we need to take the reciprocal of the base raised to the power of 1/2.
[(1/3x)^(-1/2)] = 1/[(1/3x)^(1/2)] = 1/√(1/3x) = 1/(√1/√3x) = √3x
Now our expression is: (5/3x)^(3/2) - 2/3x + √3x
Unfortunately, we cannot factorize this expression any further because the terms do not have any common factors.