Porfavor atudenme necesito saber cmomo se resuelve estos ejercicios ayudenme por favor
Adjuntos:
![](https://es-static.z-dn.net/files/d7c/ed9743d1e2a6dc4ae22cd486bdc46112.jpg)
Dayanita3718:
Hola doy 74 puntos algun universitario?
Respuestas
Respuesta dada por:
1
1:
![\frac{3^4.14^5}{7^3.2^6.3^4} = \\ \\ \frac{14^5}{7^3.2^6}= \\ \\ \frac{14.14.14.14^2}{7.7.7.2.2.2.2.2.2} = \\ \\ \frac{14.14.14.14^2}{14.14.14.2^3} = \\ \\ \frac{14^2}{2^3} = \\ \\ \frac{196}{8}= \\ \\ \frac{49}{2} \frac{3^4.14^5}{7^3.2^6.3^4} = \\ \\ \frac{14^5}{7^3.2^6}= \\ \\ \frac{14.14.14.14^2}{7.7.7.2.2.2.2.2.2} = \\ \\ \frac{14.14.14.14^2}{14.14.14.2^3} = \\ \\ \frac{14^2}{2^3} = \\ \\ \frac{196}{8}= \\ \\ \frac{49}{2}](https://tex.z-dn.net/?f=+%5Cfrac%7B3%5E4.14%5E5%7D%7B7%5E3.2%5E6.3%5E4%7D+%3D+%5C%5C++%5C%5C++%5Cfrac%7B14%5E5%7D%7B7%5E3.2%5E6%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B14.14.14.14%5E2%7D%7B7.7.7.2.2.2.2.2.2%7D+%3D+%5C%5C++%5C%5C++%5Cfrac%7B14.14.14.14%5E2%7D%7B14.14.14.2%5E3%7D+%3D+%5C%5C++%5C%5C++%5Cfrac%7B14%5E2%7D%7B2%5E3%7D+%3D+%5C%5C++%5C%5C++%5Cfrac%7B196%7D%7B8%7D%3D++%5C%5C++%5C%5C++%5Cfrac%7B49%7D%7B2%7D+)
2:
![\frac{(7.3)^4.2}{14^3.3^6}= \\ \\ \frac{(7)^4.(3)^4.2}{14^3.3^6}= \\ \\ \frac{7^3}{14^2.3^2} = \\ \\ \frac{49.7}{196.3^2}= \\ \\ \frac{7}{4.9} = \\ \\ \frac{7}{36} \frac{(7.3)^4.2}{14^3.3^6}= \\ \\ \frac{(7)^4.(3)^4.2}{14^3.3^6}= \\ \\ \frac{7^3}{14^2.3^2} = \\ \\ \frac{49.7}{196.3^2}= \\ \\ \frac{7}{4.9} = \\ \\ \frac{7}{36}](https://tex.z-dn.net/?f=+%5Cfrac%7B%287.3%29%5E4.2%7D%7B14%5E3.3%5E6%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B%287%29%5E4.%283%29%5E4.2%7D%7B14%5E3.3%5E6%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B7%5E3%7D%7B14%5E2.3%5E2%7D+++%3D+%5C%5C++%5C%5C++%5Cfrac%7B49.7%7D%7B196.3%5E2%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B7%7D%7B4.9%7D++%3D+%5C%5C++%5C%5C++%5Cfrac%7B7%7D%7B36%7D+)
3:
![\frac{5^4.4^5.5^3.3^3}{3^3.2^6.(5^4)^3.3}= \\ \\ \frac{5^7.4^5.3^3}{3^4.2^6.5^{12}} = \\ \\ \frac{4^2}{3.5^5}= \\ \\ \frac{16}{9375} \frac{5^4.4^5.5^3.3^3}{3^3.2^6.(5^4)^3.3}= \\ \\ \frac{5^7.4^5.3^3}{3^4.2^6.5^{12}} = \\ \\ \frac{4^2}{3.5^5}= \\ \\ \frac{16}{9375}](https://tex.z-dn.net/?f=+%5Cfrac%7B5%5E4.4%5E5.5%5E3.3%5E3%7D%7B3%5E3.2%5E6.%285%5E4%29%5E3.3%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B5%5E7.4%5E5.3%5E3%7D%7B3%5E4.2%5E6.5%5E%7B12%7D%7D++%3D+%5C%5C++%5C%5C++%5Cfrac%7B4%5E2%7D%7B3.5%5E5%7D%3D++%5C%5C++%5C%5C++%5Cfrac%7B16%7D%7B9375%7D+)
4:
![\frac{2^6.(5^2)^3.3^8}{15^6.4^4}= \\ \\ \frac{5^6.3^8}{15^6.4}= \\ \\ \frac{5^6.3^8}{(3)^6(5)^6.4}= \\ \\ \frac{3^2}{4}= \\ \\ \frac{9}{4} \frac{2^6.(5^2)^3.3^8}{15^6.4^4}= \\ \\ \frac{5^6.3^8}{15^6.4}= \\ \\ \frac{5^6.3^8}{(3)^6(5)^6.4}= \\ \\ \frac{3^2}{4}= \\ \\ \frac{9}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B2%5E6.%285%5E2%29%5E3.3%5E8%7D%7B15%5E6.4%5E4%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B5%5E6.3%5E8%7D%7B15%5E6.4%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B5%5E6.3%5E8%7D%7B%283%29%5E6%285%29%5E6.4%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B3%5E2%7D%7B4%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B9%7D%7B4%7D+++++)
5:
![\frac{3^5.10^4.3^2}{5^4.(2^3)^2.3^4}= \\ \\ \frac{3^3.(5^4)(2^4)}{5^4.2^6}= \\ \\ \frac{3^3}{2^2}= \\ \\ \frac{27}{4} \frac{3^5.10^4.3^2}{5^4.(2^3)^2.3^4}= \\ \\ \frac{3^3.(5^4)(2^4)}{5^4.2^6}= \\ \\ \frac{3^3}{2^2}= \\ \\ \frac{27}{4}](https://tex.z-dn.net/?f=+%5Cfrac%7B3%5E5.10%5E4.3%5E2%7D%7B5%5E4.%282%5E3%29%5E2.3%5E4%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B3%5E3.%285%5E4%29%282%5E4%29%7D%7B5%5E4.2%5E6%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B3%5E3%7D%7B2%5E2%7D%3D+%5C%5C++%5C%5C++%5Cfrac%7B27%7D%7B4%7D++++)
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Respuesta dada por:
0
Dayanita,
Vamos paso a paso en la secuencia numérica
Aplicando propiedades operatorias de potencias
![\frac{3^4*14^5}{7^3*2^6*3^4} \\ \\ = \frac{3^4*2^5*7^5}{7^3*2^6*3^4} \\ \\ = 3^{4-4} * 2^{5-6} * 7^{5-3} \\ \\ =3^0* 2^{-1} *7^2 \\ \\ =1* \frac{1}{2} *7^2 \frac{3^4*14^5}{7^3*2^6*3^4} \\ \\ = \frac{3^4*2^5*7^5}{7^3*2^6*3^4} \\ \\ = 3^{4-4} * 2^{5-6} * 7^{5-3} \\ \\ =3^0* 2^{-1} *7^2 \\ \\ =1* \frac{1}{2} *7^2](https://tex.z-dn.net/?f=+%5Cfrac%7B3%5E4%2A14%5E5%7D%7B7%5E3%2A2%5E6%2A3%5E4%7D++%5C%5C++%5C%5C+%3D+%5Cfrac%7B3%5E4%2A2%5E5%2A7%5E5%7D%7B7%5E3%2A2%5E6%2A3%5E4%7D++%5C%5C++%5C%5C+%3D+3%5E%7B4-4%7D+%2A+2%5E%7B5-6%7D+%2A+7%5E%7B5-3%7D++%5C%5C++%5C%5C+%3D3%5E0%2A++2%5E%7B-1%7D++%2A7%5E2+%5C%5C++%5C%5C+%3D1%2A+%5Cfrac%7B1%7D%7B2%7D+%2A7%5E2)
RESULTADO FINAL
![\frac{(7*3)^4*2}{(14)^3*3^6} \\ \\ = \frac{7^4*3^4*2}{2^3*7^3*3^6} \\ \\ = 7^{4-3}* 3^{4-6} *2^{1-3} \\ \\ =7^* 3^{-2} * 2^{-2} \\ \\ = \frac{7}{3^2* 2^{2} } \frac{(7*3)^4*2}{(14)^3*3^6} \\ \\ = \frac{7^4*3^4*2}{2^3*7^3*3^6} \\ \\ = 7^{4-3}* 3^{4-6} *2^{1-3} \\ \\ =7^* 3^{-2} * 2^{-2} \\ \\ = \frac{7}{3^2* 2^{2} }](https://tex.z-dn.net/?f=++%5Cfrac%7B%287%2A3%29%5E4%2A2%7D%7B%2814%29%5E3%2A3%5E6%7D++%5C%5C++%5C%5C+%3D+%5Cfrac%7B7%5E4%2A3%5E4%2A2%7D%7B2%5E3%2A7%5E3%2A3%5E6%7D++%5C%5C++%5C%5C+%3D+7%5E%7B4-3%7D%2A++3%5E%7B4-6%7D++%2A2%5E%7B1-3%7D++%5C%5C++%5C%5C+%3D7%5E%2A+3%5E%7B-2%7D+%2A+2%5E%7B-2%7D++%5C%5C++%5C%5C+%3D+%5Cfrac%7B7%7D%7B3%5E2%2A+2%5E%7B2%7D+%7D+)
RESULTADO FINAL
![\frac{ 5^{4}* 4^5* 5^{3}* 3^{3} }{3^3*2^6*(5^4)^3*3} \\ \\ = \frac{5^{4+3}* 2^{10}*3^3}{3^ {3-1} *2^6* 5^{12} } \\ \\ = 5^{7-12}* 2^{10-6}* 3^{3-2} \\ \\ = 5^{-5}*2^8*3^1 \frac{ 5^{4}* 4^5* 5^{3}* 3^{3} }{3^3*2^6*(5^4)^3*3} \\ \\ = \frac{5^{4+3}* 2^{10}*3^3}{3^ {3-1} *2^6* 5^{12} } \\ \\ = 5^{7-12}* 2^{10-6}* 3^{3-2} \\ \\ = 5^{-5}*2^8*3^1](https://tex.z-dn.net/?f=+%5Cfrac%7B+5%5E%7B4%7D%2A++4%5E5%2A++5%5E%7B3%7D%2A++3%5E%7B3%7D+%7D%7B3%5E3%2A2%5E6%2A%285%5E4%29%5E3%2A3%7D++%5C%5C++%5C%5C+%3D+++%5Cfrac%7B5%5E%7B4%2B3%7D%2A++2%5E%7B10%7D%2A3%5E3%7D%7B3%5E+%7B3-1%7D+%2A2%5E6%2A+5%5E%7B12%7D+%7D+%5C%5C++%5C%5C+%3D+5%5E%7B7-12%7D%2A++2%5E%7B10-6%7D%2A++3%5E%7B3-2%7D++%5C%5C++%5C%5C+%3D+5%5E%7B-5%7D%2A2%5E8%2A3%5E1)
RESULTADO FINAL
![\frac{2^6*(5^2)^3*3^8}{15^6*4^4} \\ \\ = \frac{2^6*5^6*3^8}{3^6*5^6*2^8} \\ \\ = 2^{-2}* 3^{-2} *5^0 \frac{2^6*(5^2)^3*3^8}{15^6*4^4} \\ \\ = \frac{2^6*5^6*3^8}{3^6*5^6*2^8} \\ \\ = 2^{-2}* 3^{-2} *5^0](https://tex.z-dn.net/?f=+%5Cfrac%7B2%5E6%2A%285%5E2%29%5E3%2A3%5E8%7D%7B15%5E6%2A4%5E4%7D++%5C%5C++%5C%5C+%3D+%5Cfrac%7B2%5E6%2A5%5E6%2A3%5E8%7D%7B3%5E6%2A5%5E6%2A2%5E8%7D++%5C%5C++%5C%5C+%3D+2%5E%7B-2%7D%2A+3%5E%7B-2%7D++%2A5%5E0)
RESULTADO FINAL
![\frac{3^5*2^4*5^4*3^2}{5^4*2^6*3^4} \\ \\ = 3^{5+2-4} * 2^{4-6} * 5^{4-4} \\ \\ =3^3* 2^{-2} *5^0 \frac{3^5*2^4*5^4*3^2}{5^4*2^6*3^4} \\ \\ = 3^{5+2-4} * 2^{4-6} * 5^{4-4} \\ \\ =3^3* 2^{-2} *5^0](https://tex.z-dn.net/?f=+%5Cfrac%7B3%5E5%2A2%5E4%2A5%5E4%2A3%5E2%7D%7B5%5E4%2A2%5E6%2A3%5E4%7D++%5C%5C++%5C%5C+%3D+3%5E%7B5%2B2-4%7D+%2A+2%5E%7B4-6%7D+%2A+5%5E%7B4-4%7D++%5C%5C++%5C%5C+%3D3%5E3%2A+2%5E%7B-2%7D+%2A5%5E0)
RESULTADO FINAL
Vamos paso a paso en la secuencia numérica
Aplicando propiedades operatorias de potencias
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