Rút gọn rồi quy đồng 3 phân số sau
2^3 . 3 / 2^2 . 3^2 . 5
2^4 . 5^2 . 7 / 2^3 .5 . 7^2 . 11
2^3 . 2^3 . 5^3 . 7 . 8 / 3.2^4.5^3.14
Rút gọn rồi quy đồng 3 phân số sau
2^3 . 3 / 2^2 . 3^2 . 5
2^4 . 5^2 . 7 / 2^3 .5 . 7^2 . 11
2^3 . 2^3 . 5^3 . 7 . 8 / 3.2^4.5^3.14
Đáp án + giải thích bước giải :
`(2^3 . 3)/(2^2 . 3^2 . 5) = (2^2 . 2 . 3)/(2^2 . 3^2. 5) = 2/15`
`(2^4 . 5^2 . 7)/(2^3 . 5 . 7^2 . 11) = (2 . 5)/(7 . 11) = 10/77`
`(2^3 . 2^3 . 5^2 . 7 . 8)/(3 . 2^4 . 5^3 . 14) = (2^6 . 5^2 . 7 . 2^3)/(3 . 2^4 . 5^2 . 7 . 2) = (2^9 . 7)/(3 . 2^5 . 3) = 2^4/3 = 16/3`
Ta có :
`2/15 = (2 . 77)/(15 . 77) = 154/1155`
`10/77 = (10 . 15)/(77 . 15) = 150/1155`
`16/3 = (16 . 385)/(3 . 385) = 6160/1155`
$\begin{array}{l}\bullet\ \text{Rút gọn :}\\\quad\dfrac{2^3 . 3 }{2^2 . 3^2 . 5 }\\=\dfrac{(2^2.3).2}{(2^2.3).3.5}\\=\dfrac{2}{3.5}\\=\dfrac2{15}\\\quad\dfrac{2^4 . 5^2 . 7 }{2^3 .5 . 7^2 . 11}\\=\dfrac{(2^3.5.7).2.5}{(2^3.5.7).7.11}\\=\dfrac{2.5}{7.11}\\=\dfrac{10}{77}\\\quad\dfrac{2^3 . 2^3 . 5^3 . 7 . 8}{3.2^4.5^3.14}\\=\dfrac{2^3.2^3.5^3.7.2^3}{3.2^4.5^3.7.2}\\=\dfrac{2^9.5^3.7}{3.2^5.5^3.7}\\=\dfrac{(2^5.5^3.7).2^4}{(2^5.5^3.7).3}\\=\dfrac{2^4}3\\=\dfrac{16}3\\\,\\\bullet\ \text{Quy đồng :}\\\rm BCNN(15,77,3)=1155\\\to\begin{cases} \dfrac{2}{15}=\dfrac{2.77}{15.77}=\dfrac{154}{1155}\\\,\\\dfrac{10}{77}=\dfrac{10.15}{77.15}=\dfrac{150}{1155}\\\,\\\dfrac{16}3=\dfrac{16.385}{3.385}=\dfrac{6160}{1155}\end{cases} \end{array}$