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\(\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}=\frac{5^{11}.7^{11}\left(7+1\right)}{5^{11}.7^{11}\left(5.7+9\right)}=\frac{8}{44}=\frac{2}{11}\)
a, (-4) . 125 . (-25) . (-11) . (-8)
= [(-4) . (-25)] . {[125 . (-8)] . (-11)}
= 100 . 11000 = 1100000
b, (-42) . 25 . (-25) . (-5) . (-4)
= [(-42) . (-5)] . [25 . (-4)] . 25
= 210 . (-100) . 25
= -5025000
1. Tìm x, biết:
a) \(\frac{4}{x}=\frac{8}{6}\). Ta có: \(\frac{8}{6}=\frac{8:2}{6:2}=\frac{4}{3}\Rightarrow x=3\)
b) \(\frac{3}{x-5}=\frac{4}{x+2}\). Ta có: \(5-2=3\)
\(\Rightarrow x=\left(3.5\right)+\left(4.2\right)+3=15+8+3=26\)
c) \(\frac{x}{-2}=\frac{-8}{x}\Rightarrow x=\left(-8\right):\left(-2\right)=4\)
2. Rút gọn
a) \(\frac{2^4.5^2.11^2.7}{2^3.5^3.7^2.11}\Leftrightarrow\frac{2^3.2^1.5^2.11.11.7}{2^3.5^2.5^1.7.7.11}\Leftrightarrow\frac{2^1.11}{5^1.7}=\frac{22}{35}\)
b) Tương tự
c) Tương tự
\(\frac{4}{x}=\frac{8}{6}\Rightarrow x=\frac{4.6}{8}=3\)
\(\frac{3}{x-5}=\frac{-4}{x+2}\Rightarrow3\left(x+2\right)=-4\left(x-5\right)\)
\(\Rightarrow3x+6=-4x+20\)
\(\Rightarrow3x+4x=20-6\)
\(\Rightarrow7x=14\)
\(\Rightarrow x=2\)
\(\frac{x}{-2}=\frac{-8}{x}\Rightarrow x^2=\left(-8\right)\left(-2\right)=16\Rightarrow x=\pm4\)
1: 243^5=(3^5)^5=3^25
3*27^8=3*(3^3)^8=3^25
=>243^5=3*27^8
6: 125^5=(5^3)^5=5^15
25^7=(5^2)^7=5^14
=>125^5>25^7(15>14)
5: 78^12-78^11=78^11(78-1)=78^11*77
78^11-78^10=78^10*77
mà 11>10
nên 78^12-78^11>78^11-78^10
`@` `\text {Ans}`
`\downarrow`
`-75.57 + 75.34 - ( 57.34 - 57.75 )`
`= -75 . 57 + 75.34 - 57.34 + 57.75`
`= 75.( - 57 + 34 + 57) + 75.34`
`= 75.34 + 75.34`
`= (75.34) .2`
`= 2550 . 2`
`= 5100`
_______
\(-11.45 - (-11).25 - ( 29.3+29.17 )\)
`= -11. (45 - 25) - 29(3 + 17)`
`= -11.20 - 29.20`
`= 20. (-11 - 29)`
`= 20. (-40)`
`= -80`
_______
\(-12.7 -72.(-12) - ( 25.55-25.43 )\)
`= -12. (7 - 72) - 25( 55 - 43)`
`= -12.(-65) - 25.12`
`= 12.65 - 25 . 12`
`= 12(65 - 25)`
`= 12.40`
`= 480`