Mejia Chadwick
02/10/2023 · Junior High School
a) \( y=x^{x^{3}(x+\cos (3 x))^{2}} \) b) \( y=(x \operatorname{sen} x)^{x \operatorname{sen}^{2} x} \)
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Para resolver estas dos ecuaciones, primero simplificaremos las expresiones dadas.
a) \( y=x^{x^{3}(x+\cos (3 x))^{2}} \)
Para simplificar esta expresión, primero simplificaremos el término \( x^{3}(x+\cos (3 x))^{2} \). Luego, elevaremos \( x \) a la potencia resultante.
b) \( y=(x \operatorname{sen} x)^{x \operatorname{sen}^{2} x} \)
Para simplificar esta expresión, primero simplificaremos el término \( x \operatorname{sen} x \). Luego, elevaremos \( x \) a la potencia resultante.
Vamos a simplificar cada una de las expresiones.
Simplify the expression by following steps:
- step0: Solution:
\(x^{3}\left(x+\cos\left(3x\right)\right)^{2}\)
- step1: Calculate:
\(x^{3}\left(x^{2}+2x\cos\left(3x\right)+\cos^{2}\left(3x\right)\right)\)
Calculate or simplify the expression \( x^{3}(x^{2}+2x\cos(3x)+\cos^{2}(3x)) \).
Simplify the expression by following steps:
- step0: Solution:
\(x^{3}\left(x^{2}+2x\cos\left(3x\right)+\cos^{2}\left(3x\right)\right)\)
La expresión \( (x\sin(x))^{x\sin^{2}(x)} \) no se puede simplificar directamente. Sin embargo, podemos expresarla de manera más compacta utilizando la notación de potencias.
Por lo tanto, las expresiones simplificadas son:
a) \( y=x^{x^{3}(x+\cos (3 x))^{2}} \)
b) \( y=(x\sin(x))^{x\sin^{2}(x)} \)
Quick Answer
a) Simplificar \( y=x^{x^{3}(x+\cos (3 x))^{2}} \).
b) Simplificar \( y=(x\sin(x))^{x\sin^{2}(x)} \).
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