(3/4)⁶×(16/3)⁶÷(16/9)⁶÷(2/3)⁶

asked by guest
on Oct 23, 2024 at 1:33 pm



You asked:

Evaluate the expression: \(\frac{\frac{{\left( \frac{3}{4} \right)}^{6} \cdot {\left( \frac{16}{3} \right)}^{6}}{{\left( \frac{16}{9} \right)}^{6}}}{{\left( \frac{2}{3} \right)}^{6}}\)

MathBot Answer:

\[\frac{\frac{{\left( \frac{3}{4} \right)}^{6} \cdot {\left( \frac{16}{3} \right)}^{6}}{{\left( \frac{16}{9} \right)}^{6}}}{{\left( \frac{2}{3} \right)}^{6}} = \frac{387420489}{262144} = 1477.891880035400390625\]

\[\begin{aligned}\frac{\frac{{\left( \frac{3}{4} \right)}^{6} \cdot {\left( \frac{16}{3} \right)}^{6}}{{\left( \frac{16}{9} \right)}^{6}}}{{\left( \frac{2}{3} \right)}^{6}}& = \left(\frac{3}{4}\right)^{6} \cdot \left(\frac{16}{3}\right)^{6} \cdot \frac{1}{\left(\frac{16}{9}\right)^{6}} \cdot \frac{1}{\left(\frac{2}{3}\right)^{6}}\\& = \frac{729}{4096} \cdot \left(\frac{16}{3}\right)^{6} \cdot \frac{1}{\left(\frac{16}{9}\right)^{6}} \cdot \frac{1}{\left(\frac{2}{3}\right)^{6}}\\& = \frac{729}{4096} \cdot \frac{16777216}{729} \cdot \frac{1}{\left(\frac{16}{9}\right)^{6}} \cdot \frac{1}{\left(\frac{2}{3}\right)^{6}}\\& = \frac{729}{4096} \cdot \frac{16777216}{729} \cdot \frac{1}{\frac{16777216}{531441}} \cdot \frac{1}{\left(\frac{2}{3}\right)^{6}}\\& = \frac{729}{4096} \cdot \frac{16777216}{729} \cdot \frac{531441}{16777216} \cdot \frac{1}{\left(\frac{2}{3}\right)^{6}}\\& = \frac{729}{4096} \cdot \frac{16777216}{729} \cdot \frac{531441}{16777216} \cdot \frac{1}{\frac{64}{729}}\\& = \frac{729}{4096} \cdot \frac{16777216}{729} \cdot \frac{387420489}{1073741824}\\& = 4096 \cdot \frac{387420489}{1073741824}\\& = \frac{387420489}{262144}\end{aligned}\]

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