(81/16)^(-3)/4*(25/9)^-3/2/ (5/2)^-3

asked by guest
on Oct 20, 2024 at 5:52 am



You asked:

Evaluate the expression: \(\frac{\frac{\frac{{\left( \frac{81}{16} \right)}^{-3}}{4} \cdot {\left( \frac{25}{9} \right)}^{-3}}{2}}{{\left( \frac{5}{2} \right)}^{-3}}\)

MathBot Answer:

\[\frac{\frac{\frac{{\left( \frac{81}{16} \right)}^{-3}}{4} \cdot {\left( \frac{25}{9} \right)}^{-3}}{2}}{{\left( \frac{5}{2} \right)}^{-3}} = \frac{64}{91125} = 0.000\overline{702331961591220850480109739368998628257887517146776406035665294924554183813443072}\]

\[\begin{aligned}\frac{\frac{\frac{{\left( \frac{81}{16} \right)}^{-3}}{4} \cdot {\left( \frac{25}{9} \right)}^{-3}}{2}}{{\left( \frac{5}{2} \right)}^{-3}}& = \frac{1}{\left(\frac{81}{16}\right)^{3}} \cdot \frac{1}{4} \cdot \frac{1}{\left(\frac{25}{9}\right)^{3}} \cdot \frac{1}{2} \cdot \frac{1}{\frac{1}{\left(\frac{5}{2}\right)^{3}}}\\& = \frac{4096}{531441} \cdot \frac{1}{4} \cdot \frac{1}{\left(\frac{25}{9}\right)^{3}} \cdot \frac{1}{2} \cdot \frac{1}{\frac{1}{\left(\frac{5}{2}\right)^{3}}}\\& = \frac{4096}{531441} \cdot \frac{1}{4} \cdot \frac{729}{15625} \cdot \frac{1}{2} \cdot \frac{1}{\frac{1}{\left(\frac{5}{2}\right)^{3}}}\\& = \frac{4096}{531441} \cdot \frac{1}{4} \cdot \frac{729}{15625} \cdot \frac{1}{2} \cdot \frac{1}{\frac{8}{125}}\\& = \frac{4096}{531441} \cdot \frac{1}{4} \cdot \frac{729}{15625} \cdot \frac{125}{16}\\& = \frac{1024}{531441} \cdot \frac{729}{15625} \cdot \frac{125}{16}\\& = \frac{1024}{11390625} \cdot \frac{125}{16}\\& = \frac{64}{91125}\end{aligned}\]

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