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Bài 1:
a) \(\left(x-3\right)^5=32\)
⇒ \(\left(x-3\right)^5=2^5\)
⇒ \(x-3=2\)
⇒ \(x=2+3\)
⇒ \(x=5\)
Vậy \(x=5.\)
b) \(\left(x^3\right)^{12}=x\)
⇒ \(x^{36}=x\)
⇒ \(x^{36}-x=0\)
⇒ \(x.\left(x^{35}-1\right)=0\)
⇒ \(\left[{}\begin{matrix}x=0\\x^{35}-1=0\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x=0\\x^{35}=0+1\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x=0\\x^{35}=1\end{matrix}\right.\)
⇒ \(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
Vậy \(x\in\left\{0;1\right\}.\)
Chúc bạn học tốt!
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c: \(=\dfrac{7}{23}\cdot\left(\dfrac{-4}{3}-\dfrac{5}{2}\right)=\dfrac{7}{23}\cdot\dfrac{-8-15}{6}\)
\(=\dfrac{7}{23}\cdot\dfrac{-23}{6}=-\dfrac{7}{6}\)
d: \(=\dfrac{5}{7}\left(23+\dfrac{1}{4}-13-\dfrac{1}{4}\right)=\dfrac{5}{7}\cdot10=\dfrac{50}{7}\)
e: \(=\dfrac{2^5\cdot3^3\cdot5^3}{2^3\cdot3^3\cdot2^2\cdot5^2}=5\)
i: \(=\dfrac{1}{3^{10}}\cdot3^{50}-\dfrac{2^{10}}{3^{10}}:\dfrac{4^5}{3^{10}}\)
\(=3^{40}-1\)
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a, \(\dfrac{20}{x}=\dfrac{-12}{15}\Rightarrow x=\dfrac{20.15}{-12}\Rightarrow x=-25\)
\(b,\dfrac{-15}{35}=\dfrac{27}{x}\Rightarrow x=\dfrac{35.27}{-15}\Rightarrow x=-63\)
\(c,\dfrac{\dfrac{4}{5}}{1\dfrac{2}{5}}=\dfrac{2\dfrac{2}{5}}{x}\Rightarrow x=\dfrac{2\dfrac{2}{5}.1\dfrac{2}{5}}{\dfrac{4}{5}}\Rightarrow x=\dfrac{\dfrac{84}{25}}{\dfrac{4}{5}}\Rightarrow x=\dfrac{21}{5}\)
\(d,\dfrac{x}{1\dfrac{1}{4}}=\dfrac{1\dfrac{1}{5}}{2}\Rightarrow x=\dfrac{1\dfrac{1}{4}.1\dfrac{1}{5}}{2}\Rightarrow x=\dfrac{\dfrac{3}{2}}{2}\Rightarrow x=\dfrac{3}{4}\)
\(e,\dfrac{\dfrac{1}{2}}{1\dfrac{1}{4}}=\dfrac{x}{3\dfrac{1}{3}}\Rightarrow x=\dfrac{\dfrac{1}{2}.3\dfrac{1}{3}}{1\dfrac{1}{4}}\Rightarrow x=\dfrac{\dfrac{5}{3}}{\dfrac{5}{4}}\Rightarrow x=\dfrac{4}{3}\)