Question

What is the simplified form of the expression?

Answer 1

Remember
(x^m)/(x^n)=x^(m-n)

(q^(33/4))/(q^8)=q^((33/4)-8)
what is 33/4-8?
33/4-8=33/4-32/4=1/4

result is
q^1/4 or $\sqrt[4]{q}$

answer is $q^{ \frac{1}{4} }$

Answer 2

$\frac{q^{\frac{33}{4}}}{q^{8}} = \frac{\sqrt[4]{q^{33}}}{q^{8}} = \frac{q^{8}\sqrt[4]{q}}{q^{8}} = \sqrt[4]{q}$