Tính hợp lí
a) \(10.\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
b) 1 + 2 + 22 + 23 + 24 +...+ 299 + 2100
giúp mình với huuhu
Tính hợp lí :
a ) 10 . \(\frac{4^6.9^5+6^9.120}{8^4.3^{12}.6^{11}}\)
Sửa đề : \(10.\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(10\cdot\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)
\(=10\cdot\frac{2^{12}\cdot3^{10}+2\cdot9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=10\cdot\frac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\cdot\left(2\cdot3-1\right)}\)
\(=10\cdot\frac{2\cdot6}{3\cdot5}=8\)
Bài làm:
\(10.\frac{4^6.9^5+6^9.120}{8^4.3^{12}.6^{11}}\)
\(=\frac{2.5.2^{12}.3^{10}+2^9.3^9.2.5.2^2.3}{2^{12}.3^{12}.2^{11}.3^{11}}\)
\(=\frac{2^{13}.3^{10}.5+2^{12}.3^{10}.5}{2^{23}.3^{23}}\)
\(=\frac{2^{12}.3^{10}.5\left(2+1\right)}{2^{23}.3^{23}}\)
\(=\frac{2^{12}.3^{11}.5}{2^{23}.3^{23}}=\frac{5}{2^{11}.3^{12}}\)
sợ sai
Tính hợp lí:
\(10\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
ai giúp tớ với
tính hợp lí:
\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
Biến đổi ra đi , ví dụ : 46=(22)6=22x6=212
Còn cách trình bày thì viết kiểu phân số , đánh trên máy tính ko quen nhé , mong bạn thông cảm
tính hợp lí:
a) A = 10\(\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
b) B = 5+53+55+...+599
tính = cách hợp lí nếu có thể :
\(\frac{10^3+2.5^3+5^3}{55}-\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(\frac{10^3+2.5^3+5^3}{55}-\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)\(=\frac{2^3.5^3+2.5^3+5^3}{5.11}-\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\frac{5^3\left(2^3+2+1\right)}{5.11}-\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{5^2.11}{11}-\frac{2.6}{3.5}=25-\frac{4}{5}=\frac{121}{5}\)
\(\dfrac{-4^6.9^5-6^9.120}{-8^4.3^{12}-6^{11}}\)
\(=\dfrac{-2^{12}\cdot3^{10}-2^{12}\cdot3^{10}\cdot5}{-2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}=\dfrac{2^{12}\cdot3^{10}\cdot6}{2^{11}\cdot3^{11}\cdot7}=\dfrac{2\cdot6}{3\cdot7}=\dfrac{12}{21}=\dfrac{4}{7}\)
.\(10.\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
Giải:
\(10.\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=10.\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=10.\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=10.\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(2.3-1\right)}\)
\(=10.\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}\)
\(=10.\dfrac{2^{13}.3^{11}}{2^{11}.3^{11}.5}\)
\(=10.\dfrac{2^2}{5}\)
\(=2^3=8\)
Vậy ...
Rút gọn biểu thức: \(A=\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}\)
\(=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.5}\)
\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}=\dfrac{2.6}{3.5}=\dfrac{4}{5}\)
\(A=\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{\left(2^2\right)^6.\left(3^2\right)^5+6^9.6.2^2.5}{\left(2^3\right)^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\dfrac{2^{11}.3^{10}\left(2^1+2^1.5\right)}{2^{11}.3^{10}\left(2^1.3^2-1.3^1\right)}=\dfrac{2+10}{2.9-1.3}=\dfrac{12}{15}=\dfrac{4}{5}\)
Tính hợp lý:
\(10.\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
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