Answer
$a)$ $s^{5/4}$
$b)$ $\dfrac{3y}{x}$
Work Step by Step
$a)$ $\sqrt{s\sqrt{s^{3}}}$
Rewrite the roots as powers with rational exponent:
$\sqrt{s\sqrt{s^{3}}}=(s\cdot s^{3/2})^{1/2}=...$
Evaluate the product inside the parentheses:
$...=(s^{1+3/2})^{1/2}=(s^{5/2})^{1/2}=...$
Finally, evaluate the power:
$...=s^{5/4}$
$b)$ $\sqrt[3]{\dfrac{54x^{2}y^{4}}{2x^{5}y}}$
Rewrite the cubic root as a power with rational exponent:
$\sqrt[3]{\dfrac{54x^{2}y^{4}}{2x^{5}y}}=\Big(\dfrac{54x^{2}y^{4}}{2x^{5}y}\Big)^{1/3}=...$
Evaluate the division inside the parentheses:
$...=(27x^{2-5}y^{4-1})^{1/3}=(27x^{-3}y^{3})^{1/3}=...$
Finally, evaluate the power and simplify if possible:
$...=3x^{-1}y=\dfrac{3y}{x}$
