(4^3.4^2)^3
You asked:
Evaluate the expression: \({{4}^{{3.4}^{2}}}^{3}\)
MathBot Answer:
\[{{4}^{{3.4}^{2}}}^{3} = 590295810358705651712 \cdot 2^{\frac{9}{25}} \approx 757600930237243682564.93508133685077697527785021582244\]
\[\begin{aligned}{{4}^{{3.4}^{2}}}^{3}& = \left(4^{\left(3 + \frac{4}{10}\right)^{2}}\right)^{3}\\& = \left(4^{\left(3 + \frac{2}{5}\right)^{2}}\right)^{3}\\& = \left(4^{\left(\frac{17}{5}\right)^{2}}\right)^{3}\\& = \left(4^{\frac{289}{25}}\right)^{3}\\& = \left(8388608 \cdot 2^{\frac{3}{25}}\right)^{3}\\& = 590295810358705651712 \cdot 2^{\frac{9}{25}}\end{aligned}\]