To evaluate [tex]\(49^{\frac{1}{3}}\)[/tex], we are effectively looking for the cube root of 49. Let's break down the steps involved to understand this process:
1. Understanding the Expression:
- The given expression is [tex]\(49^{\frac{1}{3}}\)[/tex].
- The exponent [tex]\(\frac{1}{3}\)[/tex] indicates that we are finding the cube root of 49.
2. Cube Root Concept:
- The cube root of a number [tex]\(x\)[/tex] is a value [tex]\(y\)[/tex] such that when [tex]\(y\)[/tex] is raised to the power of 3, we get [tex]\(x\)[/tex]. Mathematically, [tex]\(y = x^{\frac{1}{3}}\)[/tex] implies [tex]\(y^3 = x\)[/tex].
3. Application to the Given Value:
- We need to find a number [tex]\(y\)[/tex] such that [tex]\(y^3 = 49\)[/tex].
4. Calculation of [tex]\(49^{\frac{1}{3}}\)[/tex]:
- Through a detailed evaluation and understanding of cube roots, we find that the cube root of 49 is approximately 3.659.
Therefore, the value of [tex]\(49^{\frac{1}{3}}\)[/tex] is:
[tex]\[ 49^{\frac{1}{3}} \approx 3.659 \][/tex]
So, the final evaluated result for [tex]\(49^{\frac{1}{3}}\)[/tex] is approximately [tex]\(3.6593057100229713\)[/tex].
