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\(\dfrac{72^3.54^2}{108^4}\)
\(=\dfrac{18^3.4^3.18^2.3^2}{18^4.6^4}\)
\(=\dfrac{18^5.2^6.3^2}{18^4.2^4.3^4}\)
\(=\dfrac{18.2^2}{3^2}\)
\(=\dfrac{9.2.2^2}{9}\)
\(=2^3=8\)
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a, \(B=\dfrac{2^{10}.13+2^{10}.65}{2^8.104}\)
\(=\dfrac{2^{10}.\left(13+65\right)}{2^8.2^3.13}\)
\(=\dfrac{2^{10}.78}{2^{11}.13}\)\(=\dfrac{1.6}{2.1}=\dfrac{1.3}{1.1}=3\)
b: \(=\dfrac{2^{20}\cdot3^2+2^{54}}{2^{18}\cdot5^2}=\dfrac{2^{20}\left(3^2+2^{32}\right)}{2^{18}\cdot5^2}=\dfrac{2^2\left(3^2+2^{32}\right)}{25}\)
c: \(=\dfrac{2^9\cdot3^6\cdot3^6\cdot2^2}{2^8\cdot3^{12}}=\dfrac{2^{11}}{2^8}=8\)
d: \(=\dfrac{2^{12}\cdot3^4\cdot3^{10}}{2^{12}\cdot3^{12}}=9\)
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a)4^10x8^15=(2^2)10x(2^3)15
=22x10x23x15
= 220x245
=220+45
=265
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Để giải bài toán này, chúng ta sẽ tính từng phần và sau đó kết hợp kết quả cuối cùng.
72^3 = 72 * 72 * 72 = 373248 54^2 = 54 * 54 = 2916 108^4 = 108 * 108 * 108 * 108 = 16777216
Bây giờ, ta thay các giá trị này vào biểu thức:
(72^3 * 54^2) / 108^4 = (373248 * 2916) / 16777216
Tiếp theo, ta thực hiện phép tính trong ngoặc, sau đó chia cho 16777216:
(373248 * 2916) / 16777216 = 1088391168 / 16777216
Kết quả là 64.8.
Vậy, giá trị của biểu thức là 64.8.
\(\dfrac{72^3\cdot54^2}{108^4}=\dfrac{\left(2^3\cdot3^2\right)^3\cdot\left(2\cdot3^3\right)^2}{\left(2^2\cdot3^3\right)^4}=\dfrac{2^9\cdot3^6\cdot2^2\cdot3^6}{2^8\cdot3^{12}}\)
\(=\dfrac{2^{11}\cdot3^{12}}{2^8\cdot3^{12}}=2^3=8\)
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a) \(\dfrac{a}{5}=\dfrac{b}{4}\Rightarrow\dfrac{a^2}{25}=\dfrac{b^2}{16}\)
Áp dụng tính chất DTSBN :
\(\dfrac{a^2}{25}=\dfrac{b^2}{16}=\dfrac{a^2-b^2}{25-16}=\dfrac{1}{9}\)
\(\Rightarrow\left\{{}\begin{matrix}a^2=\dfrac{1}{9}\cdot25=\dfrac{25}{9}\\b^2=\dfrac{1}{9}\cdot16=\dfrac{16}{9}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=\dfrac{5}{3};b=\dfrac{4}{3}\\a=\dfrac{-5}{3};b=-\dfrac{4}{3}\end{matrix}\right.\)
Vậy \(\left(a;b\right)\in\left\{\left(\dfrac{5}{3};\dfrac{4}{3}\right);\left(-\dfrac{5}{3};-\dfrac{4}{3}\right)\right\}\)
b) \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}\Rightarrow\dfrac{a^2}{4}=\dfrac{b^2}{9}=\dfrac{c^2}{16}\)
Áp dụng tính chất DTSBN :
\(\dfrac{a^2}{4}=\dfrac{b^2}{9}=\dfrac{c^2}{16}=\dfrac{2c^2}{32}=\dfrac{a^2-b^2+2c^2}{4-9+32}=\dfrac{108}{27}=4\)
\(\Rightarrow\left\{{}\begin{matrix}a^2=4.4=16\\b^2=4.9=36\\c^2=4,16=64\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=4;=6;c=8\\a=-4;b=-6;c=-8\end{matrix}\right.\)
Vậy (a;b;c) \(\in\left\{\left(4;6;8\right);\left(-4;-6;-8\right)\right\}\)
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Sửa \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}\)
Đặt \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=k\Rightarrow a=2k;b=3k;c=4k\)
\(a^2-b^2+2c^2=108\\ \Rightarrow4k^2-9k^2+32k^2=108\\ \Rightarrow27k^2=108\Rightarrow k^2=4\\ \Rightarrow\left[{}\begin{matrix}k=2\\k=-2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4;y=6;z=8\\x=-4;y=-6;z=-8\end{matrix}\right.\)
Ta có:
\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{a^2}{2^2}=\dfrac{b^2}{3^2}=\dfrac{2c^2}{2.4^2}=\dfrac{a^2}{4}=\dfrac{b^2}{9}=\dfrac{2c^2}{32}\)
Áp dụng tcdtsbn , ta có:
\(\dfrac{a^2}{4}=\dfrac{b^2}{9}=\dfrac{2c^2}{32}=\dfrac{a^2-b^2+2c^2}{4-9+32}=\dfrac{108}{27}=4\)
\(\Rightarrow\left\{{}\begin{matrix}a=8\\b=12\\c=16\end{matrix}\right.\)
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tham khảo!!
https://lazi.vn/edu/exercise/tim-cac-so-a-b-c-biet-rang-a-2-b-3-c-4-va-a-2-b-2-2c-2-108
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1. \(\frac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}=\frac{3^{10}\left(11+5\right)}{3^9\cdot2^4}=\frac{3^{10}\cdot2^4}{3^9\cdot2^4}=3\)
2. \(\frac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}=\frac{2^{10}\cdot\left(13+65\right)}{2^8\cdot104}=\frac{2^{10}\cdot78}{2^8\cdot104}=\frac{2^8\cdot2^2\cdot2\cdot3\cdot13}{2^8\cdot2^3\cdot13}=\frac{2^8\cdot2^3\cdot3\cdot13}{2^8\cdot2^3\cdot13}=3\)
3. \(\frac{72^2\cdot54^2}{108^4}=\frac{\left(2^3\cdot3^2\right)^2\cdot\left(2\cdot3^3\right)^2}{\left(2^2\cdot3^3\right)^4}\)
\(=\frac{2^6\cdot3^4\cdot2^2\cdot3^6}{2^8\cdot3^{12}}=\frac{2^8\cdot3^{10}}{2^8\cdot3^{12}}=\frac{3^{10}}{3^{12}}=3^{-2}=\frac{1}{9}\)
4. \(\frac{21^2\cdot14\cdot125}{35^5\cdot6}=\frac{\left(3\cdot7\right)^2\cdot2\cdot7\cdot5^3}{\left(5\cdot7\right)^5\cdot2\cdot3}=\frac{3^2\cdot7^2\cdot2\cdot7\cdot5^3}{5^5\cdot7^5\cdot2\cdot3}=\frac{3^2\cdot7^3\cdot2\cdot5^3}{5^3\cdot5^2\cdot7^2\cdot7^3\cdot2\cdot3}=\frac{3^2}{5^2\cdot3\cdot7^2}=\frac{3}{1225}\)
=8
mk hỏi cách làm chứ ko nhờ bn bấm máy tính