Answer
$$(\frac{x^{n}y^{3n+1}}{y^{n}})^{3}=x^{3n}y^{6n+3}$$
Work Step by Step
$$(\frac{x^{n}y^{3n+1}}{y^{n}})^{3}$$
Simplify the term inside the parentheses.
Recall the quotient rule: $\frac{a^{m}}{a^{n}}=a^{m-n}$ and $\frac{a^{n}}{a^{m}}=\frac{1}{a^{m-n}}$
Thus,
$$\frac{x^{n}y^{3n+1}}{y^{n}}$$ $$=x^{n}y^{3n+1-{n}}$$ $$=x^{n}y^{2n+1}$$
Rewrite the equation:
$$(x^{n}y^{2n+1})^{3}$$
Products to Powers rule: $(ab)^{n} = a^{n}\cdot b^{n}$
Thus,
$$(x^{n}y^{2n+1})^{3}$$ $$=x^{(n)(3)}y^{(2n+1)(3)}$$ $$=x^{3n}y^{6n+3}$$
