Questions: (3yz^5+6)^4(3yz^5+6)^5

(3yz^5+6)^4(3yz^5+6)^5
Transcript text: $\left(3 y z^{5}+6\right)^{4}\left(3 y z^{5}+6\right)^{5}$
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Solution

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To simplify the given expression, we can use the property of exponents that states \(a^m \cdot a^n = a^{m+n}\). Here, the base is the same, so we can add the exponents.

Paso 1: Identificar la expresión base y los exponentes

La expresión dada es \((3yz^5 + 6)^4 \cdot (3yz^5 + 6)^5\). Aquí, la base es \(3yz^5 + 6\) y los exponentes son 4 y 5.

Paso 2: Aplicar la propiedad de los exponentes

Usamos la propiedad de los exponentes que dice \(a^m \cdot a^n = a^{m+n}\). Sumamos los exponentes: \[ 4 + 5 = 9 \]

Paso 3: Formar la expresión simplificada

Sustituimos la base y el exponente simplificado en la expresión: \[ (3yz^5 + 6)^9 \]

Respuesta Final

\[ \boxed{(3yz^5 + 6)^9} \]

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