To solve the problem, we need to simplify the given expression [tex]\(\sqrt[3]{27 x} + \sqrt[3]{x}\)[/tex].
1. Start by simplifying [tex]\(\sqrt[3]{27 x}\)[/tex]:
- Notice that [tex]\(27\)[/tex] is a perfect cube because [tex]\(27 = 3^3\)[/tex].
- Therefore, [tex]\(\sqrt[3]{27 x}\)[/tex] can be written as [tex]\(\sqrt[3]{27} \cdot \sqrt[3]{x}\)[/tex].
2. Knowing that [tex]\(\sqrt[3]{27} = 3\)[/tex], we can simplify this to:
[tex]\[
\sqrt[3]{27 x} = 3 \sqrt[3]{x}
\][/tex]
3. Now we have the expression simplified as:
[tex]\[
\sqrt[3]{27 x} + \sqrt[3]{x} = 3 \sqrt[3]{x} + \sqrt[3]{x}
\][/tex]
4. Combine like terms:
[tex]\[
3 \sqrt[3]{x} + \sqrt[3]{x} = 4 \sqrt[3]{x}
\][/tex]
Thus, the expression [tex]\(\sqrt[3]{27 x} + \sqrt[3]{x}\)[/tex] is equivalent to [tex]\(4 \sqrt[3]{x}\)[/tex].
The correct answer is:
A. [tex]\(4 \sqrt[3]{x}\)[/tex]
