((3/2) ^ 3 * (2/5) ^ 4)/(9/4 * (2/5) ^ 3)

asked by guest
on Oct 23, 2024 at 4:30 am



You asked:

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

MathBot Answer:

\[\frac{{\left( \frac{3}{2} \right)}^{3} \cdot {\left( \frac{2}{5} \right)}^{4}}{\frac{9}{4} \cdot {\left( \frac{2}{5} \right)}^{3}} = \frac{3}{5} = 0.6\]

\[\begin{aligned}\frac{{\left( \frac{3}{2} \right)}^{3} \cdot {\left( \frac{2}{5} \right)}^{4}}{\frac{9}{4} \cdot {\left( \frac{2}{5} \right)}^{3}}& = \left(\frac{3}{2}\right)^{3} \cdot \left(\frac{2}{5}\right)^{4} \cdot \frac{1}{\frac{9}{4} \cdot \left(\frac{2}{5}\right)^{3}}\\& = \frac{27}{8} \cdot \left(\frac{2}{5}\right)^{4} \cdot \frac{1}{\frac{9}{4} \cdot \left(\frac{2}{5}\right)^{3}}\\& = \frac{27}{8} \cdot \frac{16}{625} \cdot \frac{1}{\frac{9}{4} \cdot \left(\frac{2}{5}\right)^{3}}\\& = \frac{27}{8} \cdot \frac{16}{625} \cdot \frac{1}{\frac{9}{4} \cdot \frac{8}{125}}\\& = \frac{27}{8} \cdot \frac{16}{625} \cdot \frac{1}{\frac{18}{125}}\\& = \frac{27}{8} \cdot \frac{8}{45}\\& = \frac{3}{5}\end{aligned}\]

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