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3.
a) \(\left(x-1\right)^3=125\)
=> \(\left(x-1\right)^3=5^3\)
=> \(x-1=5\)
=> \(x=5+1\)
=> \(x=6\)
Vậy \(x=6.\)
b) \(2^{x+2}-2^x=96\)
=> \(2^x.\left(2^2-1\right)=96\)
=> \(2^x.3=96\)
=> \(2^x=96:3\)
=> \(2^x=32\)
=> \(2^x=2^5\)
=> \(x=5\)
Vậy \(x=5.\)
c) \(\left(2x+1\right)^3=343\)
=> \(\left(2x+1\right)^3=7^3\)
=> \(2x+1=7\)
=> \(2x=7-1\)
=> \(2x=6\)
=> \(x=6:2\)
=> \(x=3\)
Vậy \(x=3.\)
Chúc bạn học tốt!
a) \(\frac{75^3.3^7}{81^4.5^6}=\frac{5^3.3^3.5^3.3^7}{\left(3^4\right)^4.5^6}=\frac{5^6.3^3.3^7}{3^{16}.5^6}=\frac{3^{10}}{3^{16}}=\frac{1}{3^6}=\frac{1}{729}\)
b) \(\frac{6^6.4^2}{3^{12}.2^8}=\frac{2^6.3^6.\left(2^2\right)^2}{3^{12}.2^8}=\frac{2^6.3^6.2^4}{3^{12}.2^8}=\frac{2^{10}.3^6}{3^{12}.2^8}=\frac{2^2.1}{3^6}=\frac{4}{729}\)
c) \(\frac{34^5.2^5}{2^{14}.17^5}=\frac{2^5.17^5.2^5}{2^{14}.17^5}=\frac{2^{10}}{2^{14}}=\frac{1}{2^4}=\frac{1}{16}\)
`@` `\text {Ans}`
`\downarrow`
`a,`
`5.125.25 \div 5^6`
`=`\(5\cdot5^3\cdot5^2\div5^6\)
`=`\(5^{1+3+2-6}=5^{6-6}=5^0=1\)
`b,`
\(2^{14}\div\left(2^6\cdot32\right)\)
`=`\(2^{14}\div\left(2^6\cdot2^5\right)\)
`=`\(2^{14}\div2^{11}=2^3\)
`c,`
`3.3^5\div 27`
`=`\(3\cdot3^5\div3^3\)
`=`\(3^{1+5-3}\)
`=`\(3^3\)
`d,`
\(2^{15}\div\left(2^6\cdot32\right)=2^{15}\div\left(2^6\cdot2^5\right)=2^{15}\div2^{11}=2^4\)
`e,`
\(3^2\cdot27\div81=3^2\cdot3^3\div3^4=3\)
`g,`
\(100\cdot1000\cdot10000-10^9=10^2\cdot10^3\cdot10^4-10^9\)
`=`\(10^9-10^9=0\)
`h,`
\(125^4\div5^9=\left(5^3\right)^4\div5^9=5^{12}\div5^9=5^3\)
a) 1
b) 8
c) 27
d) 16
e) 3
g) 0
h) 125