To find the simplified form of [tex]\(27^{\frac{1}{3}}\)[/tex], we need to determine the cube root of 27.
Here are the steps to solve this:
1. Recognize that [tex]\(27\)[/tex] is a perfect cube. In other words, it can be expressed as [tex]\(a^3\)[/tex] for some integer [tex]\(a\)[/tex].
2. Identify the base number [tex]\(a\)[/tex] such that [tex]\(a^3 = 27\)[/tex].
[tex]\[
a^3 = 27
\][/tex]
3. Determine the value of [tex]\(a\)[/tex]. We can test integers to find that:
[tex]\[
3^3 = 3 \times 3 \times 3 = 27
\][/tex]
4. Therefore, [tex]\(a = 3\)[/tex].
5. Substituting [tex]\(a\)[/tex] back, we get:
[tex]\[
27^{\frac{1}{3}} = 3
\][/tex]
Thus, the simplified form of [tex]\(27^{\frac{1}{3}}\)[/tex] is [tex]\(3\)[/tex].
