To solve the expression [tex]\(\sqrt[3]{3^3 x^3 y^{15}}\)[/tex], we will simplify it step-by-step by applying the cube root to each term.
1. Identify the expression inside the cube root:
[tex]\[
\sqrt[3]{3^3 x^3 y^{15}}
\][/tex]
2. Separate the expression into distinct parts:
[tex]\[
\sqrt[3]{3^3 \cdot x^3 \cdot y^{15}}
\][/tex]
3. Apply the cube root to each part individually:
- For [tex]\(3^3\)[/tex]:
[tex]\[
\sqrt[3]{3^3} \Rightarrow 3
\][/tex]
- For [tex]\(x^3\)[/tex]:
[tex]\[
\sqrt[3]{x^3} \Rightarrow x
\][/tex]
- For [tex]\(y^{15}\)[/tex]:
[tex]\[
\sqrt[3]{y^{15}} = y^{15/3} \Rightarrow y^5
\][/tex]
4. Combine the simplified terms:
[tex]\[
3 \cdot x \cdot y^5 = 3xy^5
\][/tex]
So, the simplified form of [tex]\(\sqrt[3]{3^3 x^3 y^{15}}\)[/tex] is:
[tex]\[
3xy^5
\][/tex]
Thus, the final answer is:
[tex]\[
\boxed{3xy^5}
\][/tex]
