Rút gọn phân số sau thành phân số tối giản:
a, \(\dfrac{5^3.90.4^3}{25^2.3^22^{13}}\)
b, \(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}\)
c, \(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\)
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TN
9 tháng 8 2015
\(\frac{2.3.\left(1+2.3+7.7\right)}{3.5.\left(1+2.3+7.7\right)}=\frac{2}{5}\)
11 tháng 7 2017
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) \(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\) = \(\dfrac{2.3+2^2.2.3+2.7.3.7}{3.5+3.2.5.2+3.7.5.7}\) = \(\dfrac{2.3+2^3.3+2.3}{3.5+3.5.2^2+3.5}\) = \(\dfrac{2.3 \left(1+2^2+1\right)}{3.5\left(1+2^2+1\right)}\) = \(\dfrac{2.3}{3.5}\) = \(\dfrac{2}{5}\)
PA
10 tháng 7 2016
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
BY
10 tháng 7 2016
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) \(\frac{2\cdot3+4\cdot6+14\cdot21}{3\cdot5+6\cdot10+21\cdot35}=\frac{2\cdot3+2^2\cdot2\cdot3+2\cdot3\cdot7^2}{3\cdot5+2^2\cdot3\cdot5+3\cdot5\cdot7^2}=\frac{2\cdot3\left(1+2^2+7^2\right)}{3\cdot5\left(1+2^2+7^2\right)}=\frac{2}{5}\)
9 tháng 8 2016
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
9 tháng 8 2016
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
24 tháng 5 2022
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
HC
23 tháng 8 2017
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. \(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}=\dfrac{15^2.16^3\left(16-15\right)}{12^2.20^2\left(20-12\right)}=\dfrac{15^2.16^3}{12^2.20^2.8}=\dfrac{\left(3.5\right)^2.\left(2^4\right)^3}{\left(3.2^2\right)^2.\left(2^2.5\right)^2.2^3}=\dfrac{3^2.5^2.2^{12}}{3^2.2^4.2^4.5^2.2^3}=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^{11}}=\dfrac{1}{2}\)
23 tháng 8 2017
\(a\))\(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}\)
\(=\dfrac{5^3.3^2.10.\left(2^2\right)^3}{\left(5^2\right)^2.3^2.2^{13}}\Leftrightarrow\dfrac{1.1.10.1}{5.1.2^7}=\dfrac{1}{64}\)
14 tháng 8 2016
\(\frac{5^3.2.3^2.5.2^6}{5^{10}.3^2.2^{13}}=\frac{5^4.2^7.3^2}{5^{10}.3^2.2^{13}}=\frac{1}{5^6.2^6}=\frac{1}{10^6}\)
14 tháng 8 2016
\(\frac{18\left(27-23\right)}{4\left(34-52\right)}=\frac{18.4}{4.\left(-18\right)}=-1\)
10 tháng 8 2017
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) \(\dfrac{15^5.16^7}{12^5.20^5}=\dfrac{5^5.3^5.2^{28}}{2^{10}.3^5.2^{10}.5^5}=\dfrac{5^5.3^5.2^{28}}{2^{20}.3^5.5^5}=\dfrac{2^{28}}{2^{20}}=256\)
HC
10 tháng 8 2017
\(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}=\dfrac{5^3.2.5.3^2.2^6}{5^4.3^2.2^{13}}=\dfrac{5^4.3^2.2^7}{5^4.3^2.2^{13}}=\dfrac{1}{2^6}=\dfrac{1}{64}\)
\(\dfrac{15^2.16^4.15^3.16^3}{12^2.20^3.20^2.12^3}=\dfrac{\left(3.5\right)^2.\left(2^4\right)^4.\left(3.5\right)^3.\left(2^4\right)^3}{\left(3.2^2\right)^2.\left(2^2.5\right)^3.\left(2^2.5\right)^2.\left(2^2.3\right)^3}=\dfrac{3^2.5^2.2^{16}.3^3.5^3.2^{12}}{3^2.2^4.2^6.5^3.2^4.5^2.2^6.3^3}=\dfrac{3^5.5^5.2^{28}}{3^5.5^5.2^{20}}=2^8=256\)
Giải:
a) \(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}\)
\(=\dfrac{5^3.5.3^2.2.\left(2^2\right)^3}{\left(5^2\right)^2.3^2.2^{13}}\)
\(=\dfrac{5^4.3^2.2.2^6}{5^4.3^2.2^{13}}\)
\(=\dfrac{5^4.3^2.2^7}{5^4.3^2.2^{13}}\)
\(=\dfrac{1}{2^6}=\dfrac{1}{64}\)
b) \(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}\)
\(=\dfrac{15^2.16^3.16-15^2.16^3.15}{12^2.20^2.20-20^2.12^2.12}\)
\(=\dfrac{15^2.16^3.\left(16-15\right)}{12^2.20^2.\left(20-12\right)}\)
\(=\dfrac{\left(3.5\right)^2.\left(2^4\right)^3.1}{\left(3.2^2\right)^2.\left(2^2.5\right)^2.8}\)
\(=\dfrac{3^2.5^2.2^{12}}{3^2.\left(2^2\right)^2.\left(2^2\right)^2.5^2.2^3}\)
\(=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^4.2^4.2^3}\)
\(=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^{11}}\)
\(=2\)
c) \(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\)
\(=\dfrac{2.3+2.3.2.2+2.3.7.7}{3.5+3.5.2.2+3.5.7.7}\)
\(=\dfrac{2.3+2.3.4+2.3.49}{3.5+3.5.4+3.5.49}\)
\(=\dfrac{2.3.\left(1+4+49\right)}{3.5.\left(1+4+49\right)}\)
\(=\dfrac{2.3}{3.5}\)
\(=\dfrac{2}{5}\)
Chúc bạn học tốt!