Simplify the following algebraic expressions: 5d) 3/(2x3) - (8x2y)/(2y) 5f) sqrt((16x3y2)/(3y2)) + sqrt((96)/(2))

$$\sqrt[3]{\frac{54x^3y^3}{2x^3}} - \frac{8x^2y}{2y}$$

Simplify the expression inside the cube root:

$$\frac{54x^3y^3}{2x^3} = \frac{54}{2} \cdot \frac{x^3}{x^3} \cdot y^3 = 27y^3$$

Simplify the second fraction:

$$\frac{8x^2y}{2y} = \frac{8}{2} \cdot x^2 \cdot \frac{y}{y} = 4x^2$$

$$3y - 4x^2$$

The final answer is $\boxed{3y - 4x^2}$.

5f)

$$\sqrt{\frac{16x^3y^2}{3y^2}} + \sqrt{\frac{96}{2}}$$

Simplify the expression inside the first square root:

$$\frac{16x^3y^2}{3y^2} = \frac{16x^3}{3}$$

Simplify the expression inside the second square root:

$$\frac{96}{2} = 48$$

For the first term:

$$\sqrt{\frac{16x^3}{3}} = \frac{\sqrt{16x^3}}{\sqrt{3}} = \frac{\sqrt{16x^2 \cdot x}}{\sqrt{3}} = \frac{4x\sqrt{x}}{\sqrt{3}}$$

Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{3}$:

$$\frac{4x\sqrt{x}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{4x\sqrt{3x}}{3}$$

For the second term:

$$\sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3}$$

$$\frac{4x\sqrt{3x}}{3} + 4\sqrt{3}$$

The final answer is $\boxed{\frac{4x\sqrt{3x}}{3} + 4\sqrt{3}}$.