Simplify 9 3/2 x 9 4/2 divided by 9 1/2

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Solution

$\frac{9^{3 / 2} \times 9^{4 / 2}}{9^{1 / 2}} = \frac{9^{\frac{3}{2} + \frac{4}{2}}}{9^{\frac{1}{2}}} = \frac{9^{7 / 2}}{9^{1 / 2}} = 9^{\frac{7}{2} - \frac{1}{2}} = 9^{3} = 729$

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