{(2/3)^2}^3*(1/3)^-4*(3)^-1*(6)^-1

asked by guest
on Sep 20, 2024 at 8:39 am



You asked:

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

MathBot Answer:

\[{{\left( \frac{2}{3} \right)}^{2}}^{3} \cdot {\left( \frac{1}{3} \right)}^{-4} \cdot {3}^{-1} \cdot {6}^{-1} = \frac{32}{81} = 0.\overline{395061728}\]

\[\begin{aligned}{{\left( \frac{2}{3} \right)}^{2}}^{3} \cdot {\left( \frac{1}{3} \right)}^{-4} \cdot {3}^{-1} \cdot {6}^{-1}& = \left(\left(\frac{2}{3}\right)^{2}\right)^{3} \cdot \frac{1}{(\frac{1}{3})^{4}} \cdot \frac{1}{3} \cdot \frac{1}{6}\\& = \left(\frac{4}{9}\right)^{3} \cdot \frac{1}{(\frac{1}{3})^{4}} \cdot \frac{1}{3} \cdot \frac{1}{6}\\& = \frac{64}{729} \cdot \frac{1}{(\frac{1}{3})^{4}} \cdot \frac{1}{3} \cdot \frac{1}{6}\\& = \frac{64}{729} \cdot \frac{81}{3} \cdot \frac{1}{6}\\& = \frac{64}{729} \cdot \frac{81}{18}\\& = \frac{64}{9} \cdot \frac{1}{18}\\& = \frac{32}{81}\end{aligned}\]

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