Emplea calculadora y aplicando las propiedades de las potencias, calcula el valor de:
[/tex]
![[ \frac{1}{3}] ^{7} * [ \frac{1}{3}] ^{-9} [ \frac{1}{3}] ^{7} * [ \frac{1}{3}] ^{-9}](https://tex.z-dn.net/?f=+%5B+%5Cfrac%7B1%7D%7B3%7D%5D++%5E%7B7%7D+%2A+%5B+%5Cfrac%7B1%7D%7B3%7D%5D+%5E%7B-9%7D++)
![[ \frac{10}{3}] ^{3} : [ \frac{10}{3}] ^{5} [ \frac{10}{3}] ^{3} : [ \frac{10}{3}] ^{5}](https://tex.z-dn.net/?f=+%5B+%5Cfrac%7B10%7D%7B3%7D%5D++%5E%7B3%7D+%3A+%5B+%5Cfrac%7B10%7D%7B3%7D%5D+%5E%7B5%7D++)
![3 ^{9}* 5^{3} * 3^{-7} * 5^{-4} 3 ^{9}* 5^{3} * 3^{-7} * 5^{-4}](https://tex.z-dn.net/?f=3+%5E%7B9%7D%2A++5%5E%7B3%7D+%2A+3%5E%7B-7%7D+%2A+5%5E%7B-4%7D+)
![( a^{7} a^{-4} )^{2} ( a^{7} a^{-4} )^{2}](https://tex.z-dn.net/?f=%28+a%5E%7B7%7D++a%5E%7B-4%7D+%29%5E%7B2%7D+)
porfa
Respuestas
Respuesta dada por:
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Tienes lo siguiente:
1.
![\frac{10^4}{10^{-3}}. \frac{(5^3)^{1/2}}{5^{1/2}}[(-2)^3]^2=(10^{4-(-3)})(5^{3/2-1/2})[-8]^2=\\\\(10^7)(5)(64)=320(10^7)=3,200,000,000 \frac{10^4}{10^{-3}}. \frac{(5^3)^{1/2}}{5^{1/2}}[(-2)^3]^2=(10^{4-(-3)})(5^{3/2-1/2})[-8]^2=\\\\(10^7)(5)(64)=320(10^7)=3,200,000,000](https://tex.z-dn.net/?f=+%5Cfrac%7B10%5E4%7D%7B10%5E%7B-3%7D%7D.+%5Cfrac%7B%285%5E3%29%5E%7B1%2F2%7D%7D%7B5%5E%7B1%2F2%7D%7D%5B%28-2%29%5E3%5D%5E2%3D%2810%5E%7B4-%28-3%29%7D%29%285%5E%7B3%2F2-1%2F2%7D%29%5B-8%5D%5E2%3D%5C%5C%5C%5C%2810%5E7%29%285%29%2864%29%3D320%2810%5E7%29%3D3%2C200%2C000%2C000++)
2.
![(1/3)^7*(1/3)^{-9}=(1/3)^{7-9}=(1/3)^{-2}= \frac{1}{(1/3)^2}= \frac{1}{(1/9)}=9 (1/3)^7*(1/3)^{-9}=(1/3)^{7-9}=(1/3)^{-2}= \frac{1}{(1/3)^2}= \frac{1}{(1/9)}=9](https://tex.z-dn.net/?f=%281%2F3%29%5E7%2A%281%2F3%29%5E%7B-9%7D%3D%281%2F3%29%5E%7B7-9%7D%3D%281%2F3%29%5E%7B-2%7D%3D+%5Cfrac%7B1%7D%7B%281%2F3%29%5E2%7D%3D+%5Cfrac%7B1%7D%7B%281%2F9%29%7D%3D9++)
3.
![(10/3)^3:(10/3)^5=(10/3)^{3-5}=(10/3)^{-2}=(3/10)^2=9/100=0.09 (10/3)^3:(10/3)^5=(10/3)^{3-5}=(10/3)^{-2}=(3/10)^2=9/100=0.09](https://tex.z-dn.net/?f=%2810%2F3%29%5E3%3A%2810%2F3%29%5E5%3D%2810%2F3%29%5E%7B3-5%7D%3D%2810%2F3%29%5E%7B-2%7D%3D%283%2F10%29%5E2%3D9%2F100%3D0.09)
4.
![3^9*5^3*3^{-7}*5^{-4}=3^{9-7}*5^{3-4}=3^2*5^{-1}= \frac{3^2}{5}= \frac{9}{5}=1.8 3^9*5^3*3^{-7}*5^{-4}=3^{9-7}*5^{3-4}=3^2*5^{-1}= \frac{3^2}{5}= \frac{9}{5}=1.8](https://tex.z-dn.net/?f=3%5E9%2A5%5E3%2A3%5E%7B-7%7D%2A5%5E%7B-4%7D%3D3%5E%7B9-7%7D%2A5%5E%7B3-4%7D%3D3%5E2%2A5%5E%7B-1%7D%3D+%5Cfrac%7B3%5E2%7D%7B5%7D%3D+%5Cfrac%7B9%7D%7B5%7D%3D1.8++)
5.
![(a^7a^{-4})^2=(a^{7-4})^2=(a^3)^2=a^6 (a^7a^{-4})^2=(a^{7-4})^2=(a^3)^2=a^6](https://tex.z-dn.net/?f=%28a%5E7a%5E%7B-4%7D%29%5E2%3D%28a%5E%7B7-4%7D%29%5E2%3D%28a%5E3%29%5E2%3Da%5E6)
Saludos!
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