\(S=2\cdot10+2\cdot12+2\cdot14+...+2\cdot20\)

\(S=2\cdot\left(10+12+14+16+18+20\right)\)

\(S=2\cdot\left[\left(20+10\right)\cdot6:2\right]\)

\(S=2\cdot90=180\)

\(S=2\cdot10+2\cdot12+2\cdot14+\dots+2\cdot20\\=2\cdot(10+12+14+\dots+20)\)

Đặt \(A=10+12+14+\dots+20\)

Số các số hạng của $A$ là:

$(20-10):2+1=6$ (số)

Tổng $A$ bằng:

$(20+10)\cdot6:2=90$

Thay $A=90$ vào $S$, ta được:

$S=2\cdot90=180$

S=300

Tính bình thường nhé b

S = 2.10 + 2.12 + 2.14 +...+ 2.20

S = 2.10 + 2.12 + 2.14 + 2.16 + 2.18 + 2.20

S = 20 + 24 + 28 + 32 + 36 + 40

S =(20 + 40) + (24 + 36) + (28 + 32)

S = 60 + 60 + 60

S = 180

\(S=\frac{8.2+2.14+2.90+2.6+2.12}{2.3.4+2.8+2.79+2.11}\)

     \(=\frac{2\left(8+14+90+6+12\right)}{2\left(3.4+8+79+11\right)}\)

     \(=\frac{130}{110}\)

     \(=\frac{13}{11}\)

\(S=\frac{2\cdot\left(8+14+90+6+12\right)}{2.\left(3.4+8+79+11\right)}=\frac{2.130}{2.110}=\frac{130}{110}=\frac{13}{11}\)

Nếu đúng cho L ike nhé !

\(S=\frac{2\left(8+14+90+6+12\right)}{2\cdot\left(3.4+8+79+11\right)}=\frac{130}{110}=\frac{13}{11}\)

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!

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

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

a=2

b=2/5

a=2

b=2\5 đó bạn

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

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

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

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

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

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

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

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