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Sagot :
Claro, vamos a aplicar las propiedades de los exponentes en cada uno de los casos:
### 1) [tex]\((xy)^2\)[/tex]
Aplicamos la regla de la potencia de un producto:
[tex]\[ (xy)^n = x^n \cdot y^n \][/tex]
En este caso:
[tex]\[ (xy)^2 = x^2 \cdot y^2 \][/tex]
Entonces:
[tex]\[ (xy)^2 = x^2 \cdot y^2 \][/tex]
### 2) [tex]\(\frac{a^5}{a^2}\)[/tex]
Aplicamos la regla de la división de potencias con la misma base:
[tex]\[ \frac{a^m}{a^n} = a^{m-n} \][/tex]
En este caso:
[tex]\[ \frac{a^5}{a^2} = a^{5-2} \][/tex]
Entonces:
[tex]\[ \frac{a^5}{a^2} = a^3 \][/tex]
### 3) [tex]\(\left(\frac{x}{y}\right)^3\)[/tex]
Aplicamos la regla de la potencia de un cociente:
[tex]\[ \left(\frac{x}{y}\right)^n = \frac{x^n}{y^n} \][/tex]
En este caso:
[tex]\[ \left(\frac{x}{y}\right)^3 = \frac{x^3}{y^3} \][/tex]
Entonces:
[tex]\[ \left(\frac{x}{y}\right)^3 = \frac{x^3}{y^3} \][/tex]
Por lo tanto, las respuestas son:
1) [tex]\((xy)^2 = x^2 \cdot y^2\)[/tex]
2) [tex]\(\frac{a^5}{a^2} = a^3\)[/tex]
3) [tex]\(\left(\frac{x}{y}\right)^3 = \frac{x^3}{y^3}\)[/tex]
### 1) [tex]\((xy)^2\)[/tex]
Aplicamos la regla de la potencia de un producto:
[tex]\[ (xy)^n = x^n \cdot y^n \][/tex]
En este caso:
[tex]\[ (xy)^2 = x^2 \cdot y^2 \][/tex]
Entonces:
[tex]\[ (xy)^2 = x^2 \cdot y^2 \][/tex]
### 2) [tex]\(\frac{a^5}{a^2}\)[/tex]
Aplicamos la regla de la división de potencias con la misma base:
[tex]\[ \frac{a^m}{a^n} = a^{m-n} \][/tex]
En este caso:
[tex]\[ \frac{a^5}{a^2} = a^{5-2} \][/tex]
Entonces:
[tex]\[ \frac{a^5}{a^2} = a^3 \][/tex]
### 3) [tex]\(\left(\frac{x}{y}\right)^3\)[/tex]
Aplicamos la regla de la potencia de un cociente:
[tex]\[ \left(\frac{x}{y}\right)^n = \frac{x^n}{y^n} \][/tex]
En este caso:
[tex]\[ \left(\frac{x}{y}\right)^3 = \frac{x^3}{y^3} \][/tex]
Entonces:
[tex]\[ \left(\frac{x}{y}\right)^3 = \frac{x^3}{y^3} \][/tex]
Por lo tanto, las respuestas son:
1) [tex]\((xy)^2 = x^2 \cdot y^2\)[/tex]
2) [tex]\(\frac{a^5}{a^2} = a^3\)[/tex]
3) [tex]\(\left(\frac{x}{y}\right)^3 = \frac{x^3}{y^3}\)[/tex]
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