{4^2/3*8^-3/6*2^-1/12}^1/4

asked by guest
on Jul 26, 2024 at 11:28 pm



You asked:

Evaluate the expression: \(\frac{{\left( \frac{\frac{\frac{{4}^{2}}{3} \cdot {8}^{-3}}{6} \cdot {2}^{-1}}{12} \right)}^{1}}{4}\)

MathBot Answer:

\[\frac{{\left( \frac{\frac{\frac{{4}^{2}}{3} \cdot {8}^{-3}}{6} \cdot {2}^{-1}}{12} \right)}^{1}}{4} = \frac{1}{55296} = 0.00001808449\overline{074}\]

\[\begin{aligned}\frac{{\left( \frac{\frac{\frac{{4}^{2}}{3} \cdot {8}^{-3}}{6} \cdot {2}^{-1}}{12} \right)}^{1}}{4}& = \left(4^{2} \cdot \frac{1}{3} \cdot \frac{1}{8^{3}} \cdot \frac{1}{6} \cdot \frac{1}{2} \cdot \frac{1}{12}\right)^{1} \cdot \frac{1}{4}\\& = \left(\frac{16}{3} \cdot \frac{1}{8^{3}} \cdot \frac{1}{6} \cdot \frac{1}{2} \cdot \frac{1}{12}\right)^{1} \cdot \frac{1}{4}\\& = \left(\frac{16}{3} \cdot \frac{1}{512} \cdot \frac{1}{6} \cdot \frac{1}{2} \cdot \frac{1}{12}\right)^{1} \cdot \frac{1}{4}\\& = \left(\frac{16}{3} \cdot \frac{1}{512} \cdot \frac{1}{6} \cdot \frac{1}{24}\right)^{1} \cdot \frac{1}{4}\\& = \left(\frac{1}{96} \cdot \frac{1}{6} \cdot \frac{1}{24}\right)^{1} \cdot \frac{1}{4}\\& = \left(\frac{1}{576} \cdot \frac{1}{24}\right)^{1} \cdot \frac{1}{4}\\& = \left(\frac{1}{13824}\right)^{1} \cdot \frac{1}{4}\\& = \frac{1}{13824} \cdot \frac{1}{4}\\& = \frac{1}{55296}\end{aligned}\]

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