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6. ¿Cuál es el cociente de [tex][tex]$\frac{4^5}{4^7}$[/tex][/tex]?

a) [tex][tex]$4^2$[/tex][/tex]
b) [tex][tex]$2^4$[/tex][/tex]
c) [tex][tex]$\frac{1}{4^2}$[/tex][/tex]
d) [tex][tex]$\frac{1}{4^{-2}}$[/tex][/tex]

Sagot :

GinnyAnswer
Para resolver el cociente [tex]\(\frac{4^5}{4^7}\)[/tex], debemos recordar la regla de los exponentes que establece:

[tex]\[ \frac{a^m}{a^n} = a^{m-n} \][/tex]

Aplicando esta regla, tenemos:

[tex]\[ \frac{4^5}{4^7} = 4^{5-7} \][/tex]

Calculamos el exponente:

[tex]\[ 5 - 7 = -2 \][/tex]

Por lo tanto:

[tex]\[ 4^{5-7} = 4^{-2} \][/tex]

Sabemos que una base elevada a un exponente negativo es igual al recíproco de la base elevada al exponente positivo:

[tex]\[ 4^{-2} = \frac{1}{4^2} \][/tex]

Finalmente, vemos que [tex]\(\frac{1}{4^2}\)[/tex] es el resultado correcto.

Por lo tanto, la respuesta es:

c) [tex]\(\frac{1}{4^2}\)[/tex]
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