Usando as propriedades da potenciação, simplificar e dar a resposta na forma de potências de números primos:
12^5.20^3/30^4
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![(12^5.20^3)\div30^4= \\ \\ (2^2.3)^5.(2^2.5)^3]\div(2,3.5)^4= \\ \\ (2^{10}.3^5.2^6.5^3)\div2^4.3^4.5^4= \\ \\ 2^{16}.3^5.5^3)\div2^4.3^45^4= \\ \\ 2^{16-4}.3^{5-4}.5^{3-4}= \\ \\ 2^{12}.3.5^{-1}=](https://tex.z-dn.net/?f=%2812%5E5.20%5E3%29%5Cdiv30%5E4%3D+%5C%5C++%5C%5C+%282%5E2.3%29%5E5.%282%5E2.5%29%5E3%5D%5Cdiv%282%2C3.5%29%5E4%3D+%5C%5C++%5C%5C++%282%5E%7B10%7D.3%5E5.2%5E6.5%5E3%29%5Cdiv2%5E4.3%5E4.5%5E4%3D+%5C%5C++%5C%5C+2%5E%7B16%7D.3%5E5.5%5E3%29%5Cdiv2%5E4.3%5E45%5E4%3D+%5C%5C++%5C%5C+2%5E%7B16-4%7D.3%5E%7B5-4%7D.5%5E%7B3-4%7D%3D+%5C%5C++%5C%5C+2%5E%7B12%7D.3.5%5E%7B-1%7D%3D "(12^5.20^3)\div30^4= \\ \\ (2^2.3)^5.(2^2.5)^3]\div(2,3.5)^4= \\ \\ (2^{10}.3^5.2^6.5^3)\div2^4.3^4.5^4= \\ \\ 2^{16}.3^5.5^3)\div2^4.3^45^4= \\ \\ 2^{16-4}.3^{5-4}.5^{3-4}= \\ \\ 2^{12}.3.5^{-1}=")
xandegrpotclgf:
Obrigado, agora entendi
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