27^1/3×8^6/18/3^2/3

asked by guest
on Sep 19, 2024 at 3:13 pm



You asked:

Evaluate the expression: \(\frac{\frac{\frac{\frac{{27}^{1}}{3} \cdot {8}^{6}}{18}}{{3}^{2}}}{3}\)

MathBot Answer:

\[\frac{\frac{\frac{\frac{{27}^{1}}{3} \cdot {8}^{6}}{18}}{{3}^{2}}}{3} = \frac{131072}{27} = 4854.\overline{518}\]

\[\begin{aligned}\frac{\frac{\frac{\frac{{27}^{1}}{3} \cdot {8}^{6}}{18}}{{3}^{2}}}{3}& = 27^{1} \cdot \frac{1}{3} \cdot 8^{6} \cdot \frac{1}{18} \cdot \frac{1}{3^{2}} \cdot \frac{1}{3}\\& = \frac{27}{3} \cdot 8^{6} \cdot \frac{1}{18} \cdot \frac{1}{3^{2}} \cdot \frac{1}{3}\\& = \frac{27}{3} \cdot \frac{262144}{18} \cdot \frac{1}{3^{2}} \cdot \frac{1}{3}\\& = \frac{27}{3} \cdot \frac{262144}{18} \cdot \frac{1}{9} \cdot \frac{1}{3}\\& = \frac{27}{3} \cdot \frac{262144}{18} \cdot \frac{1}{27}\\& = 9 \cdot \frac{262144}{18} \cdot \frac{1}{27}\\& = \frac{2359296}{18} \cdot \frac{1}{27}\\& = \frac{131072}{27}\end{aligned}\]

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