To simplify the expression \(\frac{\sqrt{63}}{28z^8}\), let's break it down step by step:
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Simplify \(\sqrt{63}\): \[ 63 = 9 \times 7 = 3^2 \times 7 \] Therefore, \[ \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7} \]
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Substitute back into the expression: \[ \frac{\sqrt{63}}{28z^8} = \frac{3\sqrt{7}}{28z^8} \]
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Simplify the fraction: Next, we'll simplify \(\frac{3}{28}\): \[ \frac{3\sqrt{7}}{28z^8} = \frac{3}{28} \cdot \frac{\sqrt{7}}{z^8} \]
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Final expression: The simplified expression is: \[ \frac{3\sqrt{7}}{28z^8} \]
Thus, the final simplified result is: \[ \frac{3\sqrt{7}}{28z^8} \]
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