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⋅32⋅3−3−27−3335⋅23{9}^{-3} \cdot {3}^{2} \cdot {3}^{-3} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3}

MathBot Answer:

9−3⋅32⋅3−3−27−3335⋅23=129140155282429536481≈0.0004572473425019684494207899553{9}^{-3} \cdot {3}^{2} \cdot {3}^{-3} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3} = \frac{129140155}{282429536481} \approx 0.0004572473425019684494207899553

9−3⋅32⋅3−3−27−3335⋅23=1729⋅32⋅3−3−27−3335⋅23=1729⋅9⋅3−3−27−3335⋅23=181⋅3−3−27−3335⋅23=181⋅127−27−3335⋅23=12187−27−3335⋅23=12187−119683335⋅23=12187−119683275⋅23=12187−11968314348907⋅23=12187−1282429536481⋅23=12187−1282429536481⋅8=12187−8282429536481=129140155282429536481\begin{aligned}{9}^{-3} \cdot {3}^{2} \cdot {3}^{-3} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3}&=\frac{1}{729} \cdot {3}^{2} \cdot {3}^{-3} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3}\\&=\frac{1}{729} \cdot 9 \cdot {3}^{-3} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3}\\&=\frac{1}{81} \cdot {3}^{-3} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3}\\&=\frac{1}{81} \cdot \frac{1}{27} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3}\\&=\frac{1}{2187} - \frac{{27}^{-3}}{{{3}^{3}}^{5}} \cdot {2}^{3}\\&=\frac{1}{2187} - \frac{\frac{1}{19683}}{{{3}^{3}}^{5}} \cdot {2}^{3}\\&=\frac{1}{2187} - \frac{\frac{1}{19683}}{{27}^{5}} \cdot {2}^{3}\\&=\frac{1}{2187} - \frac{\frac{1}{19683}}{14348907} \cdot {2}^{3}\\&=\frac{1}{2187} - \frac{1}{282429536481} \cdot {2}^{3}\\&=\frac{1}{2187} - \frac{1}{282429536481} \cdot 8\\&=\frac{1}{2187} - \frac{8}{282429536481}\\&=\frac{129140155}{282429536481}\end{aligned}

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