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!

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

a=2

b=2/5

a=2

b=2\5 đó bạn

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

b) \(\frac{15^2.16^3.\left(16-15\right)}{12^2.20^2.\left(20-12\right)}=\frac{15^2.16^3}{12^2.20^2.8}=\frac{3^2.5^2.4^3.4^3}{4^2.3^2.4^2.5^2.8}=\frac{1}{8}\)

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

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

\(\frac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}=\frac{3^25^2.4^3.4^3-3^3.5^3.4^3.4^3}{3^2.4^2.4^3.5^3-4^2.5^2.3^3.4^3}\)

\(=\frac{3^2.5^2.4^3.4^3\left(4.4-3.5\right)}{3^2.5^2.4^3.4^2\left(5-4\right)}\)\(=\frac{4.1}{1}=4\)

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

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

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

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

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