\(\frac{5^3.90.4^3}{25^2.3^2.2^{13}}=\frac{5^3.2.3^2.5.\left(2^2\right)^3}{\left(5^2\right)^2.3^2.2^{13}}=\frac{5^4.2^7.3^2}{5^4.3^2.2^{13}}=\frac{2^7}{2^{13}}=\frac{1}{64}\)

2.3 + 4.6 + 14.21 / 3.5 + 6.10 + 21.35

= 2.3.(1 + 2.2 + 7.7) / 3.5.(1 + 2.2 + 7.7)

= 2/5

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

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

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

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

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

\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}=\frac{2.\left(3+2.6+7.21\right)}{5.\left(3+2.6+7.21\right)}=\frac{2}{5}\)

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

\(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\)

\(=\dfrac{6+24+294}{15+60+735}\)

\(=\dfrac{324}{810}\)

\(=\dfrac{2}{5}\)

\(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}=\dfrac{2.3+\left(2.3\right).2^2+\left(2.3\right).7^2}{3.5+\left(3.5\right).2^2+\left(3.5\right).7^2}\\ \\ \\ \\ =\dfrac{2.3.\left(1+2^2+7^2\right)}{3.5.\left(1+2^2+7^2\right)}\\ \\ \\ \\ =\dfrac{2.3}{3.5}=\dfrac{2}{5}\)

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

a=2

b=2/5

a=2

b=2\5 đó bạn