Respuesta:
Explicación paso a paso:
Potencia = [tex][base]^{exponente}[/tex]
[tex]5^{4}[/tex] base: 5 ; exponente: 4
[tex]2^{8}[/tex] base: 2 ; exponente: 8
[tex]7^{-9}[/tex] base: 7 ; exponente: -9
Aplica:
El producto de potencias de igual base, es
es igual a una sola base, elevada a la suma
de los exponentes de las potencias
C) [tex]\frac{3^{-2+1+5} .7^{2-4} }{3^{-1+4} .7^{3-3} } = \frac{3^{4} .7^{-2} }{3^{3} .7^{0} } = 3^{4-3} .7^{-2} } = 3^{1} .[\frac{1}{7^{2} } ] = \frac{3}{49}[/tex]
(D) y (E) son similares a (C)
F) [tex]\frac{ (3.5)^{2}.3^{2}.5^{-3}.(9.5)^{2} }{5^{2} . 5^{3} . 5^{3}.3^{3} }[/tex]
[tex]\frac{ 3^{2} .5^{2}.3^{2}.5^{-3}.(3^{2})^{2} .5^{2} }{5^{2+3+3} . 3^{3} }[/tex]
[tex]\frac{ 3^{2+2+4} .5^{2-3+2} }{5^{2+3+3} . 3^{3} }[/tex]
[tex]\frac{ 3^{8} .5^{1} }{5^{8} . 3^{3} } = 3^{8-3} .5^{1-8} = 3^{5}.5^{-7} =\frac{3^{5} }{5^{7} }[/tex]
G) [tex]\frac{ 2.3.(3.2^{2})^{3}.(2.3^{2} )^{2}. 3^{2} . (4.27)^{2} }{(3^{3} )^{2}.3^{2}.2^{4} . 3.16.3.12 }[/tex]
[tex]\frac{ 2.3.3^{2} .2^{6}.2^{2} .3^{4} . 3^{2} . (4)^{2} .(27)^{2} }{3^{6}.3^{2}.2^{4} . 3.2^{4} .3.3.2^{2} }[/tex]
[tex]\frac{ 2^{1+6+2} .3^{1+2+4+2} . (2^{2} )^{2} .(3^{3} )^{2} }{3^{6+2+1+1+1}.2^{4+4+2} }[/tex]
[tex]\frac{ 2^{9} .3^{9} . 2^{4} .3^{6} }{3^{11}.2^{10}} = \frac{ 2^{9+4} .3^{9+6} }{3^{11}.2^{10}} = 3^{15-11}.2^{13-10} = 3^{4}.2^{3} = 81.8 = 648[/tex]
