bài 3:
a: \(2\cdot4\cdot16\cdot32\cdot2^3=2\cdot2^2\cdot2^4\cdot2^5\cdot2^3=2^4\cdot2^6\cdot2^5=2^{15}\)
b: \(\left(4\cdot2^5\right):\left(2^3\cdot\frac{1}{16}\right)=2^5\cdot2^2:\frac{2^3}{16}=2^7\cdot\frac{16}{8}=2^7\cdot2=2^8\)
c: \(\frac{2^2\cdot4\cdot3^2}{2^2\cdot2^5}=\frac{2^4\cdot3^2}{2^7}=\frac{3^2}{2^3}=\frac98\)
Bài 5:
a: \(\left(x-5\right)^2=25\)
=>\(\left[\begin{array}{l}x-5=5\\ x-5=-5\end{array}\right.\Rightarrow\left[\begin{array}{l}x=10\\ x=5-5=0\end{array}\right.\)
b: \(\left(1-x\right)^5=32\)
=>1-x=2
=>x=1-2
=>x=-1
c: \(9^{x+1}-5\cdot3^{2x}=324\)
=>\(9\cdot9^{x}-5\cdot9^{x}=324\)
=>\(4\cdot9^{x}=324\)
=>\(9^{x}=81=9^2\)
=>x=2
d: \(3\cdot5^{2x+1}-3\cdot25^{x}=300\)
=>\(15\cdot5^{2x}-3\cdot5^{2x}=300\)
=>\(12\cdot25^{x}=300\)
=>\(25^{x}=25\)
=>x=1
e: \(\left(\frac47\right)^4\cdot x=\left(\frac47\right)^6\)
=>\(x=\left(\frac47\right)^6:\left(\frac47\right)^4=\left(\frac47\right)^2=\frac{16}{49}\)
f: \(3^{x+1}=3^2\)
=>x+1=2
=>x=1
