To solve the expression [tex]\(6^{2 / 5}\)[/tex], let's break it down step by step:
1. Understand the expression: We have a base of 6 raised to the power of [tex]\(\frac{2}{5}\)[/tex].
2. Fractional exponent concept: A fractional exponent indicates both a root and a power. Specifically, [tex]\(a^{m/n}\)[/tex] means:
- Take the [tex]\(n\)[/tex]-th root of [tex]\(a\)[/tex], and then
- Raise the result to the [tex]\(m\)[/tex]-th power, or
- Raise [tex]\(a\)[/tex] to the [tex]\(m\)[/tex]-th power, and then
- Take the [tex]\(n\)[/tex]-th root of that result.
3. In our expression [tex]\(6^{2/5}\)[/tex]:
- [tex]\(2/5\)[/tex] suggests taking the 5th root of 6 first, and then squaring the result, or
- Squaring 6 first and then taking the 5th root of that result.
4. Adjusted Calculation Steps:
- Let's suppose we first compute using the 5th root and then squaring the result:
[tex]\[
6^{2/5}
\][/tex]
5. Result: After appropriately using the above approach, the result of [tex]\(6^{2/5}\)[/tex] is approximately [tex]\(2.0476725110792193\)[/tex].
6. Final answer: Therefore, [tex]\(6^{2/5}\)[/tex] is equivalent to approximately [tex]\(2.0476725110792193\)[/tex].
