\(\frac{2.3.\left(1+2.3+7.7\right)}{3.5.\left(1+2.3+7.7\right)}=\frac{2}{5}\)

a=2

b=2/5

a=2

b=2\5 đó bạn

Rút gọn phân số sau thành phân số tối giản

a) \(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}\) = \(\dfrac{5^3.3^2.2.5.2^6}{5^4.3^2.2^{13}}\) = \(\dfrac{5^4.3^2.2^7}{5^4.3^2.2^{13}}\) = \(\dfrac{2^7}{2^{13}}\) = \(\dfrac{1}{2^6}\) = \(\dfrac{1}{64}\)

b) \(\dfrac{18.27+18.\left(-23\right)}{34.4-4.52}\) = \(\dfrac{18\left(27-23\right)}{4\left(34-52\right)}\) = \(\dfrac{18.4}{4.\left(-18\right)}\) = \(\dfrac{18}{-18}\) = -1

c) \(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}\) = \(\dfrac{15^2.16^3.16-15^2.15.16^3}{12^2.20^2.20-20^2.12^2.12}\) = \(\dfrac{15^2.16^3.\left(16-15\right)}{12^2.20^2.\left(20-12\right)}\)= \(\dfrac{15^2.16^3}{12^2.20^2.8}\) = \(\dfrac{\left(3.5\right)^2.\left(2^4\right)^3}{\left(3.4\right)^2.\left(4.5\right)^2.2^3}\) = \(\dfrac{3^2.5^2.2^{12}}{3^2.4^2.4^2.5^2.2^3}\) = \(\dfrac{2^{12}}{4^4.2^3}\) = \(\dfrac{2^{12}}{2^8.2^3}\) = \(\dfrac{2^{12}}{2^{11}}\) = 2

d) \(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\) = \(\dfrac{2.3+2^2.2.3+2.7.3.7}{3.5+3.2.5.2+3.7.5.7}\) = \(\dfrac{2.3+2^3.3+2.3}{3.5+3.5.2^2+3.5}\) = \(\dfrac{2.3 \left(1+2^2+1\right)}{3.5\left(1+2^2+1\right)}\) = \(\dfrac{2.3}{3.5}\) = \(\dfrac{2}{5}\)

a.

\(\frac{5^3\times90\times4^3}{25^2\times3^2\times2^{13}}=\frac{5^3\times5\times9\times2\times\left(2^2\right)^3}{\left(5^2\right)^2\times3^2\times2^{13}}=\frac{5^4\times3^2\times2\times2^6}{5^4\times3^2\times2^{13}}=\frac{1}{2^6}=\frac{1}{64}\)

b.

\(\frac{18\times27+18\times\left(-23\right)}{34\times4-4\times52}=\frac{18\times\left(27-23\right)}{4\times\left(34-52\right)}=\frac{18\times4}{4\times\left(-18\right)}=-1\)

c.

\(\frac{15^2\times16^4-15^3\times16^3}{12^2\times20^3-20^2\times12^3}=\frac{16^3\times15^2\times\left(16-15\right)}{12^2\times20^2\times\left(20-12\right)}=\frac{16\times\left(16\times15\right)^2}{8\times\left(20\times12\right)^2}=\frac{16\times240^2}{8\times240^2}=2\)

d.

\(\frac{2\times3+4\times6+14\times21}{3\times5+6\times10+21\times35}=\frac{2\times3\times\left(1+2\times2+7\times7\right)}{3\times5\times\left(1+2\times2+7\times7\right)}=\frac{2}{5}\)

Chúc bạn học tốt

a) \(\frac{5^3\cdot90\cdot4^3}{25^2\cdot3^2\cdot2^{13}}=\frac{5^3\cdot2\cdot3^2\cdot5\cdot2^6}{5^4\cdot3^2\cdot2^{13}}=\frac{1}{2^6}=\frac{1}{64}\)

b) \(\frac{18\cdot27+18\cdot\left(-23\right)}{34\cdot4-4\cdot52}=\frac{18\left(27-23\right)}{4\left(34-52\right)}=\frac{9\cdot4}{2\cdot\left(-18\right)}=\frac{3^2\cdot2^2}{2\cdot2\cdot3^2\cdot\left(-1\right)}=-1\)

c) \(\frac{15^2\cdot16^4-15^3\cdot16^3}{12^2\cdot20^3-20^2\cdot12^3}=\frac{15^2\cdot16^3\left(16-15\right)}{12^2\cdot20^2\left(20-12\right)}=\frac{15^2\cdot16^3}{12^2\cdot20^2\cdot8}=\frac{3^2\cdot5^2\cdot2^{12}}{2^4\cdot3^2\cdot2^4\cdot5^2\cdot2^3}=2\)

d) \(\frac{2\cdot3+4\cdot6+14\cdot21}{3\cdot5+6\cdot10+21\cdot35}=\frac{2\cdot3+2^2\cdot2\cdot3+2\cdot3\cdot7^2}{3\cdot5+2^2\cdot3\cdot5+3\cdot5\cdot7^2}=\frac{2\cdot3\left(1+2^2+7^2\right)}{3\cdot5\left(1+2^2+7^2\right)}=\frac{2}{5}\)

bnj nên tách ra zồi làm sẽ nhanh hơn giống như rút gọn

A) 31995-81/ 42660- 108

= 31914/42552

= 3/4

B) 7.2.7.5²/ 14.2.5

= 14 . 7 . 25 / 140

= 98 . 25/140

= 2450/140

= 35/2

C) 2^2 . 3^3 . 5/ 3.2^3.5^3

= 4 . 27 . 5 / 3 . ( 2 . 5 )³

= 108 . 5 / 3. 10³

= 540 / 3000

= 9/50

f)\(\frac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2+12^3}\)=\(\frac{15^2.16^3.\left(16-15\right)}{12^2.20^3.\left(20-12\right)}=\frac{15^2.16^3}{12^2.20^2.8}=\frac{1}{8}\)

Bài 2: 

Ta có:\(\dfrac{x+46}{20}=x+\dfrac{2}{5}\)

\(\Leftrightarrow\dfrac{x+46}{20}=\dfrac{5x+2}{5}\)

=>100x+40=5x+230

=>95x=190

hay x=2

a. \(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}=\dfrac{5^3.5.3^2.2.\left(2^2\right)^3}{\left(5^2\right)^2.3^2.2^{13}}=\dfrac{5^4.3^2.2^7}{5^4.3^2.2^{13}}=\dfrac{1}{2^6}=\dfrac{1}{64}\)

b. \(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}=\dfrac{15^2.16^3\left(16-15\right)}{12^2.20^2\left(20-12\right)}=\dfrac{15^2.16^3}{12^2.20^2.8}=\dfrac{\left(3.5\right)^2.\left(2^4\right)^3}{\left(3.2^2\right)^2.\left(2^2.5\right)^2.2^3}=\dfrac{3^2.5^2.2^{12}}{3^2.2^4.2^4.5^2.2^3}=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^{11}}=\dfrac{1}{2}\)

\(a\))\(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}\)

\(=\dfrac{5^3.3^2.10.\left(2^2\right)^3}{\left(5^2\right)^2.3^2.2^{13}}\Leftrightarrow\dfrac{1.1.10.1}{5.1.2^7}=\dfrac{1}{64}\)

a)\(\dfrac{5^{3^{ }}.90.4^3}{25^{2^{ }}3^2.2^{13}}=\dfrac{5^3.2.5.3^{2^{ }}.2^6}{5^4.3^2.2^{10}}=\dfrac{5^4.2^7.3^2}{5^4.3^2.2^{10}}=\dfrac{2^7}{2^{10}}=\dfrac{1}{8}\)

b)\(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}=\dfrac{15^2.16^3.16-15^2.15.16^3}{12^2.20^2.20-20^212^2.12}=\dfrac{15^2.16^3.\left(16-15\right)}{12^2.20^2.\left(20-12\right)}=\dfrac{15^2.16^3}{12^2.20^2.8}=\dfrac{\left(3.5\right)^2.\left(4.4\right)^3}{\left(3.4\right)^2.\left(4.5\right)^2.2^3}=\dfrac{3^2.5^2.2^{12}}{3^2.4^2.4^2.5^2.2^3}=\dfrac{2^{12}}{4^{4^{ }}.2^3}=\dfrac{2^{12}}{2^8.2^3}=\dfrac{2^{12}}{2^{11}}=2\)

\(\frac{5^3.2.3^2.5.2^6}{5^{10}.3^2.2^{13}}=\frac{5^4.2^7.3^2}{5^{10}.3^2.2^{13}}=\frac{1}{5^6.2^6}=\frac{1}{10^6}\)

\(\frac{18\left(27-23\right)}{4\left(34-52\right)}=\frac{18.4}{4.\left(-18\right)}=-1\)

\(\frac{15^2.16^3\left(16-15\right)}{12^2.20^2\left(20-12\right)}=\frac{3^2.5^2.2^{12}}{2^4.3^2.2^3.2^4.5^2}=\frac{3^2.5^2.2^{12}}{2^{11}.3^2.5^2}=2\)

a) \(\dfrac{5^3.2.5.3^2.2^6}{5^4.3^2.2^{13}}=\dfrac{5^4.2^7.3^2}{5^4.3^2.2^{13}}=\dfrac{2^7}{2^{13}}=\dfrac{1}{64}\)

b) \(\dfrac{15^5.16^7}{12^5.20^5}=\dfrac{5^5.3^5.2^{28}}{2^{10}.3^5.2^{10}.5^5}=\dfrac{5^5.3^5.2^{28}}{2^{20}.3^5.5^5}=\dfrac{2^{28}}{2^{20}}=256\)

\(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}=\dfrac{5^3.2.5.3^2.2^6}{5^4.3^2.2^{13}}=\dfrac{5^4.3^2.2^7}{5^4.3^2.2^{13}}=\dfrac{1}{2^6}=\dfrac{1}{64}\)

\(\dfrac{15^2.16^4.15^3.16^3}{12^2.20^3.20^2.12^3}=\dfrac{\left(3.5\right)^2.\left(2^4\right)^4.\left(3.5\right)^3.\left(2^4\right)^3}{\left(3.2^2\right)^2.\left(2^2.5\right)^3.\left(2^2.5\right)^2.\left(2^2.3\right)^3}=\dfrac{3^2.5^2.2^{16}.3^3.5^3.2^{12}}{3^2.2^4.2^6.5^3.2^4.5^2.2^6.3^3}=\dfrac{3^5.5^5.2^{28}}{3^5.5^5.2^{20}}=2^8=256\)

\(\dfrac{5^3\cdot90\cdot4^3}{25^2\cdot3^2\cdot2^{13}}=\dfrac{5^3\cdot2\cdot3^2\cdot5\cdot\left(2^2\right)^3}{\left(5^2\right)^2\cdot3^2\cdot2^{13}}=\dfrac{5^3\cdot2\cdot3^2\cdot5\cdot2^6}{5^4\cdot3^2\cdot2^{13}}=\dfrac{5^4\cdot3^2\cdot2^7}{5^4\cdot3^2\cdot2^{13}}=\dfrac{1}{2^6}=\dfrac{1}{64}\)

\(\dfrac{15^2\cdot16^4\cdot15^3\cdot16^3}{12^2\cdot20^3\cdot20^2\cdot12^3}=\dfrac{15^5\cdot16^7}{12^5\cdot20^5}=\dfrac{\left(3\cdot5\right)^5\cdot\left(4\cdot4\right)^7}{\left(3\cdot4\right)^5\cdot\left(4\cdot5\right)^5}=\dfrac{3^5\cdot5^5\cdot4^7\cdot4^7}{3^5\cdot4^5\cdot4^5\cdot5^5}=\dfrac{3^5\cdot5^5\cdot4^{14}}{3^5\cdot4^{10}\cdot5^5}=4^4=256\)