Answer
$a)$ $2st^{11/6}$
$b)$ $x$
Work Step by Step
$a)$ $\sqrt{4st^{3}}\sqrt[6]{s^{3}t^{2}}$
Take the square root of $4$ and write the radical expressions as powers with rational exponent:
$\sqrt{4st^{3}}\sqrt[6]{s^{3}t^{2}}=(2s^{1/2}t^{3/2})(s^{1/2}t^{1/3})=...$
Evaluate the product:
$...=2s^{1/2+1/2}t^{3/2+1/3}=2st^{11/6}$
$b)$ $\dfrac{\sqrt[4]{x^{7}}}{\sqrt[4]{x^{3}}}$
Rewrite the radical expressions as powers with rational exponent:
$\dfrac{\sqrt[4]{x^{7}}}{\sqrt[4]{x^{3}}}=\dfrac{x^{7/4}}{x^{3/4}}=...$
Evaluate the division:
$...=x^{7/4-3/4}=x^{4/4}=x$
