2.5^0.2

asked by guest
on Jan 18, 2025 at 3:06 am



You asked:

Evaluate the expression: \({2.5}^{0.2}\)

MathBot Answer:

\[{2.5}^{0.2} = \frac{2^{\frac{4}{5}} \cdot \sqrt[5]{5}}{2}\]

\[\begin{aligned}{2.5}^{0.2}& = \left(2 + \frac{5}{10}\right)^{\frac{2}{10}}\\& = \left(2 + \frac{1}{2}\right)^{\frac{2}{10}}\\& = \left(\frac{5}{2}\right)^{\frac{2}{10}}\\& = \sqrt[5]{\frac{5}{2}}\\& = \frac{1}{2} \cdot 2^{\frac{4}{5}} \cdot \sqrt[5]{5}\end{aligned}\]

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