9^-3 * 3^2 * 3^-3 - (27)^-3 / (3^3)^5 * 2^3

asked by guest
on Nov 25, 2024 at 1:38 am



You asked:

Evaluate the expression: \({9}^{-3} {3}^{2} {3}^{-3} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3}\)

MathBot Answer:

\[{9}^{-3} {3}^{2} {3}^{-3} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3} = \frac{129140155}{282429536481} \approx 0.0004572473425019684494207899553\]

\[\begin{aligned}{9}^{-3} {3}^{2} {3}^{-3} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3}& = \frac{1}{9^{3}} \cdot 3^{2} \cdot \frac{1}{3^{3}} - \frac{1}{27^{3}} \cdot \frac{1}{\left(3^{3}\right)^{5}} \cdot 2^{3}\\& = \frac{1}{729} \cdot 3^{2} \cdot \frac{1}{3^{3}} - \frac{1}{27^{3}} \cdot \frac{1}{\left(3^{3}\right)^{5}} \cdot 2^{3}\\& = \frac{9}{729} \cdot \frac{1}{3^{3}} - \frac{1}{27^{3}} \cdot \frac{1}{\left(3^{3}\right)^{5}} \cdot 2^{3}\\& = \frac{9}{729} \cdot \frac{1}{27} - \frac{1}{27^{3}} \cdot \frac{1}{\left(3^{3}\right)^{5}} \cdot 2^{3}\\& = \frac{1}{81} \cdot \frac{1}{27} - \frac{1}{27^{3}} \cdot \frac{1}{\left(3^{3}\right)^{5}} \cdot 2^{3}\\& = \frac{1}{2187} - \frac{1}{27^{3}} \cdot \frac{1}{\left(3^{3}\right)^{5}} \cdot 2^{3}\\& = \frac{1}{2187} - \frac{1}{19683} \cdot \frac{1}{\left(3^{3}\right)^{5}} \cdot 2^{3}\\& = \frac{1}{2187} - \frac{1}{19683} \cdot \frac{1}{27^{5}} \cdot 2^{3}\\& = \frac{1}{2187} - \frac{1}{19683} \cdot \frac{1}{14348907} \cdot 2^{3}\\& = \frac{1}{2187} - \frac{1}{19683} \cdot \frac{8}{14348907}\\& = \frac{1}{2187} - \frac{8}{282429536481}\\& = \frac{129140155}{282429536481}\end{aligned}\]

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