To determine the expression equivalent to [tex]\(\sqrt[3]{27 x} + \sqrt[3]{x}\)[/tex], let's analyze it step by step.
Given expression:
[tex]\[
\sqrt[3]{27 x} + \sqrt[3]{x}
\][/tex]
First, we recognize that:
[tex]\[
27 = 3^3
\][/tex]
So, we can rewrite [tex]\(\sqrt[3]{27 x}\)[/tex] as:
[tex]\[
\sqrt[3]{27 x} = \sqrt[3]{3^3 \cdot x} = 3 \sqrt[3]{x}
\][/tex]
Now, substituting this back into the original expression, we have:
[tex]\[
\sqrt[3]{27 x} + \sqrt[3]{x} = 3 \sqrt[3]{x} + \sqrt[3]{x}
\][/tex]
Next, we can factor out [tex]\(\sqrt[3]{x}\)[/tex] from both terms:
[tex]\[
3 \sqrt[3]{x} + \sqrt[3]{x} = (3 + 1)\sqrt[3]{x} = 4 \sqrt[3]{x}
\][/tex]
Therefore, the expression [tex]\(\sqrt[3]{27 x} + \sqrt[3]{x}\)[/tex] simplifies to:
[tex]\[
4 \sqrt[3]{x}
\][/tex]
By comparing this with the given options, we see the correct choice is:
A. [tex]\(4 \sqrt[3]{x}\)[/tex]
Thus, the correct answer is:
[tex]\[
\boxed{4 \sqrt[3]{x}}
\][/tex]
