Rút gọn các phân số sau : a, 2^15 . 3^6 . 7/9^3 . 8^5 . 21 b, 100^2/2^4 c, 45^10 . 5^2/75^15

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1. `a, (2^15 . 3^6 . 7)/(9^3 . 8^5 . 21)`

   `= (2^15 . 3^6 . 7)/((3^2)^3 . (2^3)^5 . 3 . 7)`

   `= (2^15 . 3^6 . 7)/(3^6 . 2^15 . 3 . 7)`

   `= 1/3`

   `b, (100^2)/(2^4)`

   `= (100 . 100)/(2^4)`

   `= (2 . 2 . 25 . 2 . 2 . 25)/(2^4)`

   `= (2^4 . 25 . 25)/(2^4)`

   `= 25 . 25 = 625`

   `c, (45^10 . 5^20)/(75^15)`

   `= ((3 . 15)^10 . 5^20)/((15 . 5)^15)`

   `= (15^10 . 3^10 . 5^20)/(15^15 . 5^15)`

   `= (15^10 . 3^10 . 5^15 . 5^5)/(15^10 . 15^5 . 5^15)`

   `= (3^10 . 5^5)/(15^5)`

   `= (3^10 . 5^5)/((3 . 5)^5)`

   `= (3^10 . 5^5)/(3^5 . 5^5)`

   `= (3^10)/(3^5)`

   `= (3^5 . 3^5)/(3^5)`

   `= 3^5 = 243`

    

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2. `a, (2^{15}.3^{6}.7)/(9^{3}.8^{5}.21)`

   `=((2^3)^{5}.(3^2)^{3}.7)/(9^{3}.8^{5}.21)`

   `=(8^{5}.9^{3}.7)/(9^{3}.8^{5}.7.3)`

   `=1/3`

   `b. (100^2)/(2^4)`

   `=(2.50)^2/(2^4)`

   `=(2^{2}.50^{2})/(2^4}`

   `=(50^{2})/(2^2)`

   `=((2.25)^2)/(2^2)`

   `=(2^{2}.25^{2})/(2^2)`

   `=25^2`

   `=625`

   `c, (45^{10}.5^{20})/(75^{15})`

   `=((3.15)^{10}.5^{20})/((15.5)^{15})`

   `=(3^{10}.15^{10}.5^{20})/(15^{15}.5^{15})`

   `=(3^{10}.5^{5})/(15^{5})`

   `=(3^{10}.5^{5})/((3.5)^{5})`

   `=(3^{10}.5^{5})/(3^{5}.5^{5})`

   `=3^5`

   `=243`

    chúc học tốt

    

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