Question

Reduce la expresión. Ejercicio adjunto

Answer 1

Respuesta:

9/4

Explicación paso a paso:

Reduce la siguiente expresión:

$\sqrt{\frac{({\frac{3}{2})}^{4} \cdot{(\frac{9}{4})}^{2}}{(\frac{3}{2})\cdot(\frac{27}{8})}}$

$\sqrt{\frac{({\frac{3}{2})}^{4} \cdot{(\frac{ {3}^{2} }{ {2}^{2} })}^{2}}{(\frac{3}{2})\cdot(\frac{ {3}^{3} }{ {2}^{3} })}}$

$\sqrt{\frac{({\frac{3}{2})}^{4} \cdot{ ({( \frac{3}{2} )}^{2} )}^{2}}{(\frac{3}{2})\cdot{(\frac{3}{2})}^{3} }}$

$\sqrt{\frac{({\frac{3}{2})}^{4} \cdot{( \frac{3}{2} )}^{4}}{(\frac{3}{2})^{1} \cdot{(\frac{3}{2})}^{3} }}$

$\sqrt{\frac{({\frac{3}{2})}^{4 + 4}}{{(\frac{3}{2})}^{1 + 3} }}$

$\sqrt{\frac{({\frac{3}{2})}^{8}}{{(\frac{3}{2})}^{4} }}$

$\sqrt{\frac{\frac{ {3}^{8} }{ {2}^{8} }}{\frac{ {3}^{4} }{ {2}^{4} } }}$

$\sqrt{ \frac{ {3}^{8} \cdot {2}^{4} }{ {3}^{4} \cdot {2}^{8} } }$

$\sqrt{ \frac{ {3}^{8 - 4} }{ {2}^{8 - 4} } }$

$\sqrt{ \frac{ {3}^{4} }{ {2}^{4} } }$

$\sqrt{ \frac{ {( {3}^{2} )}^{2} }{ {( {2}^{2} )}^{2} } }$

$\sqrt{ \frac{ {(9)}^{2} }{ {(4)}^{2} } }$

$\sqrt{ {( \frac{9}{4} )}^{2} }$

$\frac{9}{4}$