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28 tháng 7 2017
\(\dfrac{9^4.2^{15}}{2^6.24^3}=\dfrac{3^8.2^{15}}{2^6.3^3.2^9}=3^5\)
GB
1
12 tháng 4 2023
\(=\dfrac{5\cdot2^{12}\cdot3^8-3^9\cdot2^{12}}{2^{15}\cdot3^{18}-2^{13}\cdot3^9}\)
\(=\dfrac{2^{12}\cdot3^8\left(5-3\right)}{2^{13}\cdot3^9\left(2^2\cdot3^9-1\right)}\)
\(=\dfrac{1}{3\cdot\left(4\cdot3^9-1\right)}\)
1
1
DN
28 tháng 10 2021
Sơ đồ thể hiện tác động tiêu cực của việc gia tăng dân số quá nhanh ở đới nóng đối với tài nguyên, môi trường.
11 tháng 7 2023
`@` `\text {Ans}`
`\downarrow`
\(\dfrac{2^8-2^3}{2^5-1}=\dfrac{2^3\left(2^5-1\right)}{2^5-1}=\dfrac{2^3}{1}=2^3=8\)
_____
\(\dfrac{4^8\cdot9^4}{6^6\cdot8^3}\)
`=`\(\dfrac{\left(2^2\right)^8\cdot\left(3^2\right)^4}{2^6\cdot3^6\cdot\left(2^3\right)^3}\)
`=`\(\dfrac{2^{16}\cdot3^8}{2^6\cdot3^6\cdot2^9}\)
`=`\(\dfrac{2^{16}\cdot3^8}{2^{15}\cdot3^6}\)
`=`\(\dfrac{3^2}{2}\) `=`\(\dfrac{9}{2}\)
______
\(\dfrac{27^4\cdot2^3-3^{10}\cdot4^3}{6^4\cdot9^3}\)
`=`\(\dfrac{\left(3^3\right)^4\cdot2^3-3^{10}\cdot\left(2^2\right)^3}{2^4\cdot3^4\cdot\left(3^2\right)^3}\)
`=`\(\dfrac{3^{12}\cdot2^3-3^{10}\cdot2^6}{2^4\cdot3^4\cdot3^6}\)
`=`\(\dfrac{3^{10}\cdot\left(3^2\cdot2^3-2^6\right)}{3^{10}\cdot2^4}\)
`=`\(\dfrac{72-2^6}{2^4}=\dfrac{8}{16}=\dfrac{1}{2}\)
ND
Nguyễn Đức Trí
VIP
11 tháng 7 2023
\(\dfrac{2^8-2^3}{2^5-1}=\dfrac{2^3\left(2^5-1\right)}{2^5-1}=2^3=8\)
\(\dfrac{4^8.9^4}{6^6.8^3}=\dfrac{2^{16}.3^8}{2^6.3^6.2^9}=2.3^2=18\)
\(\dfrac{27^4.2^3-3^{10}.4^3}{6^4.9^3}=\dfrac{3^{12}.2^3-3^{10}.2^6}{2^4.3^4.3^6}=\dfrac{2^3.3^{10}.\left(3^2-2^3\right)}{2^4.3^{10}}=\dfrac{9-8}{2}=\dfrac{1}{2}\)
17 tháng 10 2022
a: =>9^n=9
=>n=1
b: =>5^n=5
=>n=1
c: \(\Leftrightarrow\left(-27\right)^n=-243\)
=>\(\left(-3\right)^{3n}=\left(-3\right)^5\)
=>3n=5
=>n=5/3
d: =>2^n*9/2=9*2^5
=>2^n=9*2^5:9/2=2^5*2=2^6
=>n=6
4 tháng 10 2021
\(a,\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\dfrac{1}{27}=\left(\dfrac{1}{3}\right)^3\\ \Rightarrow x-\dfrac{1}{2}=\dfrac{1}{3}\Rightarrow x=\dfrac{5}{6}\\ b,\Rightarrow\left(\dfrac{3}{2}\right)^{2x-1}:\left(\dfrac{3}{2}\right)^9=\left(\dfrac{3}{2}\right)^4\\ \Rightarrow2x-1-9=4\\ \Rightarrow2x=14\Rightarrow x=7\\ c,\Rightarrow2^{x-1}+2^{x+2}=9\cdot2^5\\ \Rightarrow2^{x-1}\left(1+2^3\right)=9\cdot2^5\\ \Rightarrow2^{x-1}\cdot9=9\cdot2^5\\ \Rightarrow2^{x-1}=2^5\Rightarrow x-1=5\Rightarrow x=6\\ d,\Rightarrow\left(2x+1\right)^2=12+69=81\\ \Rightarrow\left[{}\begin{matrix}2x+1=9\\2x+1=-9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-5\end{matrix}\right.\)
27 tháng 5 2022
\(A=\left(\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}\right)-\left(\dfrac{3}{4}+\dfrac{2}{9}+\dfrac{1}{36}\right)+\dfrac{1}{64}\)
\(=\dfrac{5+9+1}{15}-\dfrac{27+8+1}{36}+\dfrac{1}{64}\)
=1/64
OY
17 tháng 8 2021
a) \(\dfrac{-5}{9}+\dfrac{3}{5}-\dfrac{3}{9}+\dfrac{-2}{5}\)
=\(\left(\dfrac{-5}{9}-\dfrac{3}{9}\right)+\left(\dfrac{3}{5}+\dfrac{-2}{5}\right)\)
=\(\dfrac{-8}{9}+\dfrac{1}{5}=-\dfrac{31}{45}\)
b) \(\dfrac{5}{17}-\dfrac{9}{15}-\dfrac{2}{17}+\dfrac{-2}{5}\)
=\(\left(\dfrac{5}{17}-\dfrac{2}{17}\right)-\left(\dfrac{9}{15}+\dfrac{2}{5}\right)\)
=\(\dfrac{3}{17}-1=\dfrac{-14}{17}\)
\(\dfrac{9^4.2^{15}}{2^6.24^3}\) = \(\dfrac{9^4.2^9}{24^3}\) = \(\dfrac{2^9.3^8}{2^9.3^3}\) = 35 = 243
\(\dfrac{9^4\cdot2^{15}}{2^6\cdot24^3}=\dfrac{\left(3^2\right)^4\cdot2^{15}}{2^6\cdot\left(8\cdot3\right)^3}=\dfrac{3^8\cdot2^{15}}{2^6\cdot8^3\cdot3^3}=\dfrac{3^8\cdot2^{15}}{2^6\cdot2^9\cdot3^3}=\dfrac{3^8\cdot2^{15}}{2^{15}\cdot3^3}=3^5=243\)