Answer:
[tex]\frac{x^3}{y^9}[/tex]Explanation:
To simplify the expression, we will use the following properties:
[tex]\begin{gathered} (x^a)^b_{}=x^{a\cdot b} \\ \frac{x^a}{x^b}=x^{a-b} \end{gathered}[/tex]Therefore, first, apply the exponent to the numerator and the denominator of the fraction:
[tex](\frac{x^2}{xy^3})^3=\frac{(x^2)^3}{(xy^3)^3}[/tex]Then, using the first property, we get:
[tex]\frac{(x^2)^3}{x^3(y^3)^3}=\frac{x^{2\cdot3}}{x^3y^{3\cdot3}}=\frac{x^6}{x^3y^9}[/tex]Finally, use the second property:
[tex]\frac{x^6}{x^3}\cdot\frac{1}{y^9}=x^{6-3}\cdot\frac{1}{y^9}=x^3\cdot\frac{1}{y^9}=\frac{x^3}{y^9}[/tex]Therefore, the simplified expression is:
[tex]\frac{x^3^{}}{y^9}[/tex]