To find the simplified form of [tex]\(27^{\frac{1}{3}}\)[/tex], we need to determine the cube root of 27. Here’s the step-by-step process:
1. Understand the notation: [tex]\(27^{\frac{1}{3}}\)[/tex] represents the cube root of 27.
2. Recall the definition of cube root: The cube root of a number [tex]\(a\)[/tex] is a number [tex]\(b\)[/tex] such that [tex]\(b^3 = a\)[/tex].
3. Identify what cubic number 27 corresponds to: We know that [tex]\(3^3 = 27\)[/tex].
4. Conclude the cube root: Since [tex]\(3^3 = 27\)[/tex], it follows that [tex]\(27^{\frac{1}{3}} = 3\)[/tex].
Therefore, the simplified form of [tex]\(27^{\frac{1}{3}}\)[/tex] is:
[tex]\[
\boxed{3}
\][/tex]
