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Propiedad de la Multiplicación de Potencias de Igual Base:

[tex]\[ a^n \times a^m = a^{n+m} \][/tex]

Ejemplo:

[tex]\[ 6^3 \times 6^4 = 6^{3+4} = 6^7 = 279936 \][/tex]

Resuelva las siguientes expresiones:

1) [tex]\[ 5^3 = 125 \][/tex]

2) [tex]\[ 3^3 \times 3^2 = 3^{3+2} = 3^5 = 243 \][/tex]

3) [tex]\[ 4^2 \times 4^3 = 4^{2+3} = 4^5 = 1024 \][/tex]

4) [tex]\[ 6^2 \times 6^3 = 6^{2+3} = 6^5 = 7776 \][/tex]

5) [tex]\[ 10^5 \times 10^2 \times 10^3 = 10^{5+2+3} = 10^{10} \][/tex]

6) [tex]\[ 8^2 \times 8^1 \times 8^3 = 8^{2+1+3} = 8^6 \][/tex]

7) [tex]\[ 9^5 \times 9^3 = 9^{5+3} = 9^8 \][/tex]

8) [tex]\[ 2^3 \times 2^5 = 2^{3+5} = 2^8 \][/tex]

9) [tex]\[ 4^3 \times 4^5 \times 4^2 = 4^{3+5+2} = 4^{10} \][/tex]

Propiedad de la División de Potencias de Igual Base:

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

Ejemplo:

[tex]\[ \frac{3^6}{3^4} = 3^{6-4} = 3^2 = 9 \][/tex]

Resuelva las siguientes expresiones:

10) [tex]\[ \frac{10^6}{10^4} = 10^{6-4} = 10^2 = 100 \][/tex]

Sagot :

GinnyAnsweridn
Claro, solucionemos el problema paso a paso utilizando la propiedad de la división de potencias de igual base.

La propiedad que utilizaremos es la siguiente:
[tex]$\frac{a^n}{a^m} = a^{n-m}$[/tex]

En este caso, los valores son:
- [tex]\(a = 3\)[/tex]
- [tex]\(n = 6\)[/tex]
- [tex]\(m = 4\)[/tex]

Aplicamos la fórmula:
[tex]\[ \frac{a^n}{a^m} = \frac{3^6}{3^4} = 3^{6-4} = 3^2 \][/tex]

Ahora, evaluamos la potencia:
[tex]\[ 3^2 = 9 \][/tex]

Por lo tanto, el resultado final es:
[tex]\[ \frac{3^6}{3^4} = 9 \][/tex]
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