Bài 1:
a. \(\frac{15^3.\left(-5\right)^4}{\left(-3\right)^5.5^6}\)
b. \(\frac{6^3.2.\left(-3\right)^2}{\left(-2\right)^9.3^7}\)
c. \(\frac{3^6.7^2-3^7.7}{3^7.21}\)
Bài 2:
a. \(\left(x-1,2\right)^2=4
\)
b.\(\left(x+1\right)^3=-125\)
c. \(\left(x-5\right)^3=2^6\)
d. \(\left(2x+1\right)^{x+1}=5^{x+1}\)
e. \(\left(5-x\right)^2+\left(5-x\right)^5=0\)
f. \(\left(1-2x\right)^4-\left(1-2x\right)^6=0\)
g. \(3^{4-x}+1=26\)
h. \(\left(7x+2\right)^{-1}=3^{-2}\)
\(a,\frac{15^3.\left(-5\right)^4}{\left(-3\right)^5.5^6}\)\(=\frac{3^3.5^3}{\left(-3\right)^5.5^2}\)\(=-\frac{5}{\left(3\right)^2}=-\frac{5}{9}\)
\(b,\frac{6^3.2.\left(-3\right)^2}{\left(-2\right)^9.3^7}\)\(=-\frac{6^3}{2^8.3^5}\)\(=-\frac{2^3.3^3}{2^8.3^5}\)\(=-\frac{1}{2^5.3^2}=-\frac{1}{288}\)
\(c,\frac{3^6.7^2-3^7.7}{3^7.21}\)\(=\frac{3^6.7\left(7-3\right)}{3^7.21}\)\(=\frac{3^6.7.4}{3^7.7.3}\)\(=\frac{4}{3.3}=\frac{4}{9}\)
\(a,\left(x-1,2\right)^2=4\)
\(\Rightarrow x-1,2=2\)
\(\Rightarrow x=3,2\)
\(b,\left(x+1\right)^3=-125\)
\(\Rightarrow\left(x+1\right)^3=\left(-5\right)^3\)
\(\Rightarrow x+1=-5\Rightarrow x=-6\)
\(c,\left(x-5\right)^3=2^6\)
\(\Rightarrow\left(x-5\right)^3=4^3\)
\(\Rightarrow x-5=4\Rightarrow x=9\)
\(d,\left(2x+1\right)^{x+1}=5^{x+1}\)
\(\Rightarrow2x+1=5\Rightarrow x=2\)
\(e,\left(5-x\right)^2+\left(5-x\right)^5=0\)
\(\Rightarrow\left(5-x\right)^2\left(1+\left(5-x\right)^3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}\left(5-x\right)^2=0\\1+\left(5-x\right)^3=0\end{cases}\Rightarrow}\orbr{\begin{cases}5-x=0\\5-x=-1\end{cases}\Rightarrow\orbr{\begin{cases}x=5\\x=6\end{cases}}}\)
\(f,\left(1-2x\right)^4-\left(1-2x\right)^6=0\)
\(\Rightarrow\left(1-2x\right)^4\left(1-\left(1-2x\right)^2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}1-2x=0\\1-2x=1\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{1}{2}\\0\end{cases}}\)
\(g,3^{4-x}-1=26\)
\(\Rightarrow3^{4-x}=27\Rightarrow3^{4-x}=3^3\Rightarrow4-x=3\Rightarrow x=1\)
Secret PersonLớp mấy mà còn sai căn bản
\(\left(x-1,2\right)^2=4\)
\(\Leftrightarrow\orbr{\begin{cases}x-1,2=\sqrt{4}\\x-1,2=-\sqrt{4}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3,2\\x=0,8\end{cases}}\)
\(\left(1-2x\right)^4-\left(1-2x\right)^6=0\)
\(\Leftrightarrow\left(1-2x\right)^4\left[\left(1-2x\right)^2-1\right]=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(1-2x\right)^4=0\\\left(1-2x\right)^2-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x\in\left\{1;0\right\}\end{cases}}\)
