Use properties of exponents to simplify.

$\small x^{\frac{1}{2}} \cdot x^{\frac{3}{2}}$

$\small x^{\frac{4}{2}}$

$x^2$

$\small x^{\frac{1}{2}}\div\left( x^{-\frac{1}{2}} \right)^3$

$\small \frac{x^{\frac{1}{2}}}{x^{-\frac{3}{2}}}$

See part (a).