Question

calcular el siguiente producto de potencia ​

Answer 1

Respuesta:

$\frac{ {( {2}^{3} )}^{2} \times {3}^{2} \times {9}^{3} }{ {2}^{4} \times {3}^{3} \times {4}^{2} } = \frac{ {( {2}^{3} )}^{2} \times {3}^{2} \times {( {3}^{3} )}^{3} }{ {2}^{4} \times {3}^{3} \times {( {2}^{2} )}^{2} } = \frac{ {2}^{6} \times {3}^{2} \times {3}^{9} }{ {2}^{4} \times {3}^{3} \times {2}^{4} } = \frac{ {2}^{6} \times {3}^{2 + 9} }{ {2}^{4 + 4} \times {3}^{3} } = \frac{ {2}^{6} \times {3}^{11} }{ {2}^{8} \times { 3}^{3} } = {2}^{ 6 - 8} \times {3}^{11 - 3} = {2}^{ - 2} \times {3}^{8} = \frac{ {3}^{8} }{ {2}^{2} }$

Answer 2

Respuesta:

$\boxed{\frac{\left(2^3\right)^2\cdot \:3^2\cdot \:9^3}{2^4\cdot \:3^3\cdot \:4^2}}$

Calcular

$\frac{3^{2} }{3^{3}} =\frac{1}{3}$

$\frac{\left(2^3\right)^2\cdot \:9^3}{2^4\cdot \:3\cdot \:4^2}$

Factorizar

$9^3=3^6$

$\frac{\left(2^3\right)^2\cdot \:3^6}{2^4\cdot \:3\cdot \:4^2}$

$\frac{3^6}{3} =3^{5}$

$\frac{\left(2^3\right)^2\cdot \:3^5}{2^4\cdot \:4^2}$

$\boxed{\frac{243}{4}}$

Saludos...