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What is the simplified form of [tex]$27^{\frac{1}{3}}$[/tex]?

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Sagot :

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]