40000(1+0.12)^2.5
You asked:
Evaluate the expression: \(40000 \cdot {\left( 1 + 0.12 \right)}^{2.5}\)
MathBot Answer:
\[40000 \cdot {\left( 1 + 0.12 \right)}^{2.5} = \frac{100352 \sqrt{7}}{5} \approx 53101.28711359075898760362882184141245\]
\[\begin{aligned}40000 \cdot {\left( 1 + 0.12 \right)}^{2.5}& = 40000 \cdot \left(1 + \frac{12}{100}\right)^{2 + \frac{5}{10}}\\& = 40000 \cdot \left(1 + \frac{3}{25}\right)^{2 + \frac{5}{10}}\\& = 40000 \cdot \left(\frac{28}{25}\right)^{2 + \frac{5}{10}}\\& = 40000 \cdot \left(\frac{28}{25}\right)^{2 + \frac{1}{2}}\\& = 40000 \cdot \left(\frac{28}{25}\right)^{\frac{5}{2}}\\& = 40000 \cdot \frac{1568}{3125} \cdot \sqrt{7}\\& = \frac{100352}{5} \cdot \sqrt{7}\end{aligned}\]