Bài 1:
`(4².25².2^5. 5^3)/(2^3. 5^2)`
`=((2^2)^2.(5^2)^2. 2^5 .5^3)/(2^3 .5^2)`
`=(2^4 .5^4 .2^5 .5^3)/(2^3 .5^2)`
`=(2^9 .5^7)/(2^3 .5^2)`
`=2^6 .5^5`
`=64.3125`
`=200 000`
Bài 2:
`a)(x-1)³=27`
`(x-1)³=3³`
`x-1=3`
`x=3+1`
`x=4`
`b)x²+x=0`
`⇔x(x+1)=0`
`⇔`\(\left[ \begin{array}{l}x=0\\x+1=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=0\\x=-1\end{array} \right.\)
`c)(2x+1)²=25`
`⇔(2x+1)²=5²`
`⇔`\(\left[ \begin{array}{l}2x+1=5\\2x+1=-5\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}2x=4\\2x=-6\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=2\\2x=-3\end{array} \right.\)
`d)(2x-3)²=9`
`⇔(2x-3)²=3²`
`⇔`\(\left[ \begin{array}{l}2x-3=3\\2x-3=-3\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}2x=3+3\\2x=-3+3\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}2x=6\\2x=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=3\\x=0\end{array} \right.\)
`e)5^(x+2)=625`
`5^(x+2)=5^4`
`x+2=4`
`x=4-2`
`x=2`
`f)(x-1)^(x+2)=(x-1)^(x+4)`
`x+2=x+4`
`x-x=4-2`
`0x=2(`ko có giá trị nào thỏa mãn `x)`
`g)(2x-1)³=-8`
`(2x-1)³=(-2)³`
`2x-1=-2`
`2x=-2+1`
`2x=-1`
`x=-1/2`
`h)1/4 . 2/6 . 3/8 . 4/10 . 5/12 ...30/62 . 31/64=2^x`
`⇒(1.2.3.4.5...30.31)/(4.6.8.10.12...62.64)=2^x`
`⇒(1.2.3.4.5...30.31)/(2.2.2.3.2.4.2.5.2.6...2.31.2.32)=2^x`
`⇒(1.2.3.4.5...30.31)/[(2.2.2.2.2...2.2).(2.3.4.5.6...31.32)]=2^x`
`⇒(1.2.3.4.5...30.31)/[2^31.(2.3.4.5.6...31.32)]=2^x`
`⇒(1.2.3.4.5...30.31)/[2^31.(2.3.4.5.6...31).32]=2^x`
`⇒1/(2^31. 32)=2^x`
`⇒1/(2^31. 2^5)=2^x`
`⇒1/(2^36)=2^x`
`⇒2^x .2^36=1`
`⇒2^(x+36)=2^0`
`⇒x+36=0`
`⇒x=0-36`
`⇒x=-36`
