\(a,\frac{20^{12}\cdot6^{14}}{8^{13}\cdot15^{12}}\)

\(=\frac{5^{12}\cdot2^{24}\cdot2^{14}\cdot3^{14}}{2^{39}\cdot3^{12}\cdot5^{12}}\)

\(=\frac{5^{12}\cdot2^{38}\cdot3^{14}}{2^{39}\cdot3^{12}\cdot5^{12}}=\frac{3^2}{2}=\frac{9}{2}\)

\(b,\frac{45^{12}\cdot10^{14}}{18^{13}\cdot25^{12}}\)

\(=\frac{5^{12}\cdot3^{24}\cdot2^{14}\cdot5^{14}}{2^{13}\cdot3^{26}\cdot5^{24}}\)

\(=\frac{5^{26}\cdot3^{24}\cdot2^{14}}{2^{13}\cdot3^{26}\cdot5^{24}}=\frac{5^2\cdot2}{3^2}=\frac{50}{9}\)

\(c,\frac{18^{12}\cdot27^8}{6^8\cdot3^{40}}\)

\(=\frac{2^{12}\cdot3^{24}\cdot3^{24}}{2^8\cdot3^8\cdot3^{40}}\)

\(=\frac{2^{12}\cdot3^{48}}{2^8\cdot3^{48}}=2^4=16\)

\(d,\frac{12^{14}\cdot9^{18}}{8^9\cdot27^{17}}\)

\(=\frac{3^{14}\cdot2^{28}\cdot3^{36}}{2^{27}\cdot3^{51}}\)

\(=\frac{3^{50}\cdot2^{28}}{2^{27}\cdot3^{51}}=\frac{2}{3}\)

làm hơi tắt nên chịu khó hiểu

\(\left(\frac{-1}{4}+\frac{7}{33}-\frac{5}{3}\right)-\left(\frac{-5}{4}+\frac{6}{11}-\frac{48}{49}\right)=\left(\frac{-1}{4}-\frac{16}{11}\right)-\left(-\frac{31}{44}-\frac{48}{49}\right)=-\frac{1}{4}-\frac{16}{11}+\frac{31}{44}+\frac{48}{49}=-\frac{1}{49}\)

yutyugubhujyikiu

\(B=\frac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}\)

\(B=\frac{1+3^4+3^8+3^{12}}{\left(1+3^4+3^8+3^{12}\right)+3^2+3^6+3^{10}+3^{14}}\)

Xét mẫu : \(\left(1+3^4+3^8+3^{12}\right)+3^2\left(1+3^4+3^8+3^{12}\right)=\left(3^2+1\right)\left(1+3^4+3^8+3^{12}\right)\)

Ta có : \(\frac{1+3^4+3^8+3^{12}}{\left(3^2+1\right)\left(1+3^4+3^8+3^{12}\right)}=\frac{1}{3^2+1}=\frac{1}{10}\)

(chủ câu hỏi)

sao lại có \(3^2+1\)ở kia

= 1/10

\(A=\frac{1+3^4+3^8+3^{12}}{1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}}\)

Ta có :

\(1+3^4+3^8+3^{12}=\left(3^{16}-1\right):\left(3^4-1\right)\)

\(1+3^2+3^4+3^6+3^8+3^{10}+3^{12}+3^{14}=\left(3^{16}-1\right):\left(3^2-1\right)\)

\(\Rightarrow A=\frac{\left(3^{16}-1\right):\left(3^4-1\right)}{\left(3^{16}-1\right):\left(3^2-1\right)}=\frac{3^2-1}{3^4-1}=\frac{1}{10}\)

help me

sao nhiều dữ vậy

\(\frac{8^{14}}{4^{12}}=\frac{\left(2^3\right)^{14}}{\left(2^2\right)^{12}}=\frac{2^{42}}{2^{24}}=2^{18}\)