Pergunta

(5x^7y^8z^10)/(10x^10)y^(9z^5)
Solução

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DianaMestre · Tutor por 5 anos
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To simplify the given expression, we can divide the numerator and denominator by their common factors.<br /><br />$\frac {5x^{7}y^{8}z^{10}}{10x^{10}y^{9}z^{5}} = \frac {5}{10} \cdot \frac {x^{7}}{x^{10}} \cdot \frac {y^{8}}{y^{9}} \cdot \frac {z^{10}}{z^{5}}$<br /><br />Simplifying each fraction separately:<br /><br />$\frac {5}{10} = \frac {1}{2}$<br /><br />$\frac {x^{7}}{x^{10}} = x^{7-10} = x^{-3}$<br /><br />$\frac {y^{8}}{y^{9}} = y^{8-9} = y^{-1}$<br /><br />$\frac {z^{10}}{z^{5}} = z^{10-5} = z^{5}$<br /><br />Putting it all together:<br /><br />$\frac {5x^{7}y^{8}z^{10}}{10x^{10}y^{9}z^{5}} = \frac {1}{2} \cdot x^{-3} \cdot y^{-1} \cdot z^{5} = \frac {z^{5}}{2x^{3}y}$<br /><br />Therefore, the simplified expression is $\frac {z^{5}}{2x^{3}y}$.
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