Which statement correctly distinguishes $5x^{1/2}$ from $(5x)^{1/2}$?

They are equal because the exponent distributes over addition.

They are equal because $5^{1/2} = 5$.

$5x^{1/2} = 5\sqrt{x}$, while $(5x)^{1/2} = \sqrt{5x}$; they are NOT equal.

$5x^{1/2} = \sqrt{5x}$, while $(5x)^{1/2} = 5\sqrt{x}$; they are NOT equal.

Which of the following is a valid application of the rational exponent distribution rule?

$(x + y)^{1/2} = x^{1/2} + y^{1/2}$

$(3x)^{1/2} = 3^{1/2} \cdot x^{1/2}$

$(x - y)^{2/3} = x^{2/3} - y^{2/3}$

$(x + 4)^{1/3} = x^{1/3} + 4^{1/3}$