Answer
$a)$ $w^{5/3}$
$b)$ $8a^{13/4}$
Work Step by Step
$a)$ $\dfrac{w^{4/3}w^{2/3}}{w^{1/3}}$
Evaluate the product in the numerator:
$\dfrac{w^{4/3}w^{2/3}}{w^{1/3}}=\dfrac{w^{4/3+2/3}}{w^{1/3}}=\dfrac{w^{6/3}}{w^{1/3}}=...$
Evaluate the division:
$...=w^{6/3-1/3}=w^{5/3}$
$b)$ $\dfrac{a^{5/4}(2a^{3/4})^{3}}{a^{1/4}}$
Raise each factor of the expression inside the parentheses to the power of $3$:
$\dfrac{a^{5/4}(2a^{3/4})^{3}}{a^{1/4}}=\dfrac{a^{5/4}(2^{3})(a^{9/4})}{a^{1/4}}=\dfrac{a^{5/4}(8)(a^{9/4})}{a^{1/4}}=...$
Evaluate the product in the numerator:
$...=\dfrac{8a^{5/4+9/4}}{a^{1/4}}=\dfrac{8a^{14/4}}{a^{1/4}}=...$
Finally, evaluate the division:
$...=8a^{14/4-1/4}=8a^{13/4}$
