como expresar como productos de potencia de numeros primos Un numero
Estos números: 25000 128 2700 3200
Respuestas
Respuesta dada por:
5
Primero descompon los números en factores primos es decir, por ejemplo:
![2500 = 5 \times 5 \times 100 = {5}^{2} \times (50 \times 2) = {5}^{2} \times( (5 \times 10) \times 2) = {5}^{2} \times ((5 \times (2 \times 5)) \times 2 = {5}^{4} \times {2}^{2} 2500 = 5 \times 5 \times 100 = {5}^{2} \times (50 \times 2) = {5}^{2} \times( (5 \times 10) \times 2) = {5}^{2} \times ((5 \times (2 \times 5)) \times 2 = {5}^{4} \times {2}^{2}](https://tex.z-dn.net/?f=2500+%3D+5+%5Ctimes+5+%5Ctimes+100+%3D++%7B5%7D%5E%7B2%7D++%5Ctimes+%2850+%5Ctimes+2%29+%3D++%7B5%7D%5E%7B2%7D++%5Ctimes%28+%285+%5Ctimes+10%29+%5Ctimes+2%29+%3D++%7B5%7D%5E%7B2%7D++%5Ctimes+%28%285+%5Ctimes+%282+%5Ctimes+5%29%29+%5Ctimes+2+%3D++%7B5%7D%5E%7B4%7D++%5Ctimes++%7B2%7D%5E%7B2%7D+)
y eso es su producto en potencias de primos
![128 = 2 \times 64 = 2 \times (8 \times 8) = 2 \times ((4 \times 2) \times (4 \times 2)) = 2 \times (((2 \times 2) \times 2) \times ((2 \times 2) \times 2)) = {2}^{7} 128 = 2 \times 64 = 2 \times (8 \times 8) = 2 \times ((4 \times 2) \times (4 \times 2)) = 2 \times (((2 \times 2) \times 2) \times ((2 \times 2) \times 2)) = {2}^{7}](https://tex.z-dn.net/?f=128+%3D+2+%5Ctimes+64+%3D+2+%5Ctimes+%288+%5Ctimes+8%29+%3D+2+%5Ctimes+%28%284+%5Ctimes+2%29+%5Ctimes+%284+%5Ctimes+2%29%29+%3D+2+%5Ctimes+%28%28%282+%5Ctimes+2%29+%5Ctimes+2%29+%5Ctimes+%28%282+%5Ctimes+2%29+%5Ctimes+2%29%29+%3D++%7B2%7D%5E%7B7%7D+)
![2700 = 3 \times900 = 3 \times (3 \times 300) = 3 \times (3 \times (3 \times 100)) = 3 \times (3 \times (3 \times (5 \times 20))) = 3 \times (3 \times (3 \times (5 \times (5 \times 4)))) = 3 \times (3 \times (3 \times (5 \times (5 \times (2 \times 2))))) = {3}^{3} \times {5}^{2} \times {2}^{2} 2700 = 3 \times900 = 3 \times (3 \times 300) = 3 \times (3 \times (3 \times 100)) = 3 \times (3 \times (3 \times (5 \times 20))) = 3 \times (3 \times (3 \times (5 \times (5 \times 4)))) = 3 \times (3 \times (3 \times (5 \times (5 \times (2 \times 2))))) = {3}^{3} \times {5}^{2} \times {2}^{2}](https://tex.z-dn.net/?f=2700+%3D+3+%5Ctimes900+%3D+3+%5Ctimes+%283+%5Ctimes+300%29+%3D+3+%5Ctimes+%283+%5Ctimes+%283+%5Ctimes+100%29%29+%3D+3+%5Ctimes+%283+%5Ctimes+%283+%5Ctimes+%285+%5Ctimes+20%29%29%29+%3D+3++%5Ctimes+%283+%5Ctimes+%283+%5Ctimes+%285+%5Ctimes+%285+%5Ctimes+4%29%29%29%29+%3D+3+%5Ctimes+%283+%5Ctimes+%283+%5Ctimes+%285+%5Ctimes+%285+%5Ctimes+%282+%5Ctimes+2%29%29%29%29%29+%3D++%7B3%7D%5E%7B3%7D++%5Ctimes++%7B5%7D%5E%7B2%7D++%5Ctimes++%7B2%7D%5E%7B2%7D+)
![3200 = 5 \times 640 = 5 \times (5 \times 128) = 5 \times (5 \times (2 \times 64)) = 5 \times (5 \times (2 \times (2 \times 32))) = 5 \times(5 \times (2 \times (2 \times (2 \times 16)))) = 5 \times (5 \times (2 \times (2 \times (2 \times (2 \times 8)))) = 5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = {5}^{2} \times {2}^{7} 3200 = 5 \times 640 = 5 \times (5 \times 128) = 5 \times (5 \times (2 \times 64)) = 5 \times (5 \times (2 \times (2 \times 32))) = 5 \times(5 \times (2 \times (2 \times (2 \times 16)))) = 5 \times (5 \times (2 \times (2 \times (2 \times (2 \times 8)))) = 5 \times 5 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = {5}^{2} \times {2}^{7}](https://tex.z-dn.net/?f=3200+%3D+5+%5Ctimes+640+%3D+5+%5Ctimes+%285+%5Ctimes+128%29+%3D+5+%5Ctimes+%285+%5Ctimes+%282+%5Ctimes+64%29%29+%3D+5+%5Ctimes+%285+%5Ctimes+%282+%5Ctimes+%282+%5Ctimes+32%29%29%29+%3D+5+%5Ctimes%285+%5Ctimes+%282+%5Ctimes+%282+%5Ctimes+%282+%5Ctimes+16%29%29%29%29+%3D+5+%5Ctimes+%285+%5Ctimes+%282+%5Ctimes+%282+%5Ctimes+%282+%5Ctimes+%282++%5Ctimes+8%29%29%29%29+%3D+5+%5Ctimes+5+%5Ctimes+2+%5Ctimes+2+%5Ctimes+2+%5Ctimes+2+%5Ctimes+2+%5Ctimes+2+%5Ctimes+2+%3D++%7B5%7D%5E%7B2%7D++%5Ctimes++%7B2%7D%5E%7B7%7D+)
cualquier duda me mandas mensaje
y eso es su producto en potencias de primos
cualquier duda me mandas mensaje
JULY1088:
muchas gracias
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