(4^3.4^2)^3

asked by guest
on Jan 24, 2025 at 8:29 am



You asked:

Evaluate the expression: 43.423{{4}^{{3.4}^{2}}}^{3}

MathBot Answer:

43.423=590295810358705651712⋅2925≈757600930237243682564.93508133685077697527785021582244{{4}^{{3.4}^{2}}}^{3} = 590295810358705651712 \cdot 2^{\frac{9}{25}} \approx 757600930237243682564.93508133685077697527785021582244

43.423=(4(3+410)2)3=(4(3+25)2)3=(4(175)2)3=(428925)3=(8388608⋅2325)3=590295810358705651712⋅2925\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}

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