To simplify the expression [tex]\(\sqrt[3]{6} \cdot \sqrt[3]{9}\)[/tex], follow these steps:
1. Recognize that when we multiply two cube roots, we can multiply the numbers inside the cube roots first. Specifically:
[tex]\[
\sqrt[3]{6} \cdot \sqrt[3]{9} = \sqrt[3]{6 \cdot 9}
\][/tex]
2. Calculate the product of the numbers inside the cube roots:
[tex]\[
6 \cdot 9 = 54
\][/tex]
3. Now we need to find the cube root of the resulting product:
[tex]\[
\sqrt[3]{54}
\][/tex]
4. The simplified result for [tex]\(\sqrt[3]{54}\)[/tex] is approximately:
[tex]\[
3.7797631496846193
\][/tex]
Thus, the expression [tex]\(\sqrt[3]{6} \cdot \sqrt[3]{9}\)[/tex] simplifies to [tex]\(\sqrt[3]{54}\)[/tex], which is approximately [tex]\(3.7797631496846193\)[/tex].
