4. (show your work and bubble the correct answer) Which expression is equivalent to (sqrt (4x^5))(sqrt (8x^4)) , where x is positive, without a perfect square factor in the radicand? A 8x^5sqrt (2x) C 2x^4sqrt (2x) B 4x^4sqrt (2x) D 4x^5sqrt (2x)

To solve this problem, we need to simplify the given expression $(\sqrt {4x^{5}})(\sqrt {8x^{4}})$.<br /><br />Step 1: Simplify each square root separately.<br />$\sqrt{4x^5} = \sqrt{4} \cdot \sqrt{x^5} = 2x^{5/2}$<br />$\sqrt{8x^4} = \sqrt{8} \cdot \sqrt{x^4} = 2x^2\sqrt{2}$<br /><br />Step 2: Multiply the simplified expressions.<br />$(2x^{5/2})(2x^2\sqrt{2}) = 4x^{5/2} \cdot x^2\sqrt{2} = 4x^{7/2}\sqrt{2}$<br /><br />Step 3: Simplify the expression further.<br />$4x^{7/2}\sqrt{2} = 4x^{4}\sqrt{2x}$<br /><br />Therefore, the correct answer is C) $4x^{4}\sqrt{2x}$.