$153.8^{2.2}$

asked by guest
on Nov 19, 2024 at 3:23 pm



You asked:

Evaluate the expression: \({153.8}^{2.2}\)

MathBot Answer:

\[{153.8}^{2.2} = \frac{591361 \cdot 5^{\frac{4}{5}} \cdot \sqrt[5]{769}}{125} \approx 64759.56725996063051388056121299699293\]


\[\begin{aligned}{153.8}^{2.2}& = \left(153 + \frac{8}{10}\right)^{2 + \frac{2}{10}}\\& = \left(153 + \frac{4}{5}\right)^{2 + \frac{2}{10}}\\& = \left(\frac{769}{5}\right)^{2 + \frac{2}{10}}\\& = \left(\frac{769}{5}\right)^{2 + \frac{1}{5}}\\& = \left(\frac{769}{5}\right)^{\frac{11}{5}}\\& = \frac{591361}{125} \cdot 5^{\frac{4}{5}} \cdot \sqrt[5]{769}\end{aligned}\]