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¿Cuál es el resultado del siguiente ejercicio?

[tex]\[
\sqrt{81}+\left(2^4 \div 2^2\right)
\][/tex]

A. 13
B. 1.1
C. 85
D. 35

Sagot :

GinnyAnswer
Para resolver el ejercicio [tex]\( \sqrt{81} + \left(2^4 \div 2^2\right) \)[/tex], sigamos estos pasos detalladamente:

1. Primero, calculemos la raíz cuadrada de 81:
[tex]\[ \sqrt{81} = 9 \][/tex]

2. Luego, resolvamos la división de potencias de 2:
[tex]\[ 2^4 \div 2^2 \][/tex]

Para esto, utilicemos la propiedad de exponente de las potencias que dice [tex]\( a^m \div a^n = a^{m-n} \)[/tex], donde [tex]\( a \)[/tex] es la base y [tex]\( m \)[/tex] y [tex]\( n \)[/tex] son los exponentes. En este caso, [tex]\( a = 2 \)[/tex], [tex]\( m = 4 \)[/tex] y [tex]\( n = 2 \)[/tex]:

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

3. Finalmente, sumemos los resultados obtenidos:
[tex]\[ 9 + 4 = 13 \][/tex]

Así que el resultado del ejercicio es:
[tex]\[ \boxed{13} \][/tex]

Por lo tanto, la respuesta correcta es: [tex]\(13\)[/tex] (opción a).
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