130*4.2^0.4
You asked:
Evaluate the expression: \(130 \cdot {4.2}^{0.4}\)
MathBot Answer:
\[130 \cdot {4.2}^{0.4} = 26 \cdot 21^{\frac{2}{5}} \cdot 5^{\frac{3}{5}} \approx 230.80386037862843284051596738305622\]
\[\begin{aligned}130 \cdot {4.2}^{0.4}& = 130 \cdot \left(4 + \frac{2}{10}\right)^{\frac{4}{10}}\\& = 130 \cdot \left(4 + \frac{1}{5}\right)^{\frac{4}{10}}\\& = 130 \cdot \left(\frac{21}{5}\right)^{\frac{4}{10}}\\& = 130 \cdot \left(\frac{21}{5}\right)^{\frac{2}{5}}\\& = 130 \cdot \frac{1}{5} \cdot 5^{\frac{3}{5}} \cdot 21^{\frac{2}{5}}\\& = 26 \cdot 5^{\frac{3}{5}} \cdot 21^{\frac{2}{5}}\end{aligned}\]