Tính nhanh:
125^7-625^5-25^9÷99
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\(\frac{\frac{1}{9}-\frac{1}{7}-\frac{1}{11}}{\frac{4}{9}-\frac{4}{7}-\frac{4}{11}}+\frac{\frac{3}{5}-\frac{3}{25}-\frac{3}{125}-\frac{3}{625}}{\frac{4}{5}-\frac{4}{25}-\frac{4}{125}-\frac{4}{625}}\)
\(=\frac{1\left(\frac{1}{9}-\frac{1}{7}-\frac{1}{11}\right)}{4.\left(\frac{1}{9}-\frac{1}{7}-\frac{1}{11}\right)}+\frac{3.\left(\frac{1}{5}-\frac{1}{25}-\frac{1}{125}-\frac{1}{625}\right)}{4.\left(\frac{1}{5}-\frac{1}{25}-\frac{1}{125}-\frac{1}{625}\right)}\)
\(=\frac{1}{4}+\frac{3}{4}=1\)
\(\frac{\frac{1}{9}-\frac{1}{7}-\frac{1}{11}}{\frac{4}{9}-\frac{4}{7}-\frac{4}{11}}+\frac{\frac{3}{5}-\frac{3}{25}-\frac{3}{125}-\frac{3}{625}}{\frac{4}{5}-\frac{4}{25}-\frac{4}{125}-\frac{4}{625}}\)
\(=\frac{\frac{1}{9}-\frac{1}{7}-\frac{1}{11}}{4\left(\frac{1}{9}-\frac{1}{7}-\frac{1}{11}\right)}+\frac{3\left(\frac{1}{5}-\frac{1}{25}-\frac{1}{125}-\frac{1}{625}\right)}{4\left(\frac{1}{5}-\frac{1}{25}-\frac{1}{125}-\frac{1}{625}\right)}\)
\(=\frac{1}{4}+\frac{3}{4}\)
=1
\(\frac{\frac{1}{9}-\frac{1}{7}-\frac{1}{11}}{\frac{4}{9}-\frac{4}{7}-\frac{4}{11}}+\frac{\frac{3}{5}-\frac{3}{25}-\frac{3}{125}-\frac{3}{625}}{\frac{4}{5}-\frac{4}{25}-\frac{4}{125}-\frac{4}{625}}\)
\(=\frac{\frac{1}{9}-\frac{1}{7}-\frac{1}{11}}{4\left(\frac{1}{9}-\frac{1}{7}-\frac{1}{11}\right)}+\frac{3\left(\frac{1}{5}-\frac{1}{25}-\frac{1}{125}-\frac{1}{625}\right)}{4\left(\frac{1}{5}-\frac{1}{25}-\frac{1}{125}-\frac{1}{625}\right)}\)
\(=\frac{1}{4}+\frac{3}{4}=\frac{4}{4}=1\)
3+3/5+3/25+3/125+3/625= 3/625x(625+125+25+5+1)= 3x781/625=2343/625
chu y: vi 3=3x625/625
3/5=3x125/125x5=3x125/625
3/25=3x25/25x25=3x25/625
3/125=3x5/125x5=3x5/625
3/625=3x1/625
cộng các kết quả trên và đặt 3/625 làm nhân từ chúng ta có kết quả như trên.
\(=\dfrac{\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}}{4\left(\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}\right)}+\dfrac{3\left(\dfrac{1}{5}-\dfrac{1}{25}-\dfrac{1}{125}-\dfrac{1}{625}\right)}{4\left(\dfrac{1}{5}-\dfrac{1}{25}-\dfrac{1}{125}-\dfrac{1}{625}\right)}\)
\(=\dfrac{1}{4}+\dfrac{3}{4}=\dfrac{4}{4}=1\)
Đặt A=3+3/5+3/25+3/125+3/625=3/5+3/5^1+3/5^2+3/5^3+3/5^4
5A=15+3+3/5^1+3/5^2+3/5^3
5A-A=(15+3+3/5^1+3/5^2+3/5^3)-(3+3/5^1+3/5^2+3/5^3+3/5^4)
4A=15-3/625=9372/625
A=2343/625
M = 1257 - 6255 - 259
M = ( 53 )7 - ( 54 )5 - ( 52 )9
M = 521 - 520 - 518
M = 518 . ( 53 - 52 - 1 )
M = 518 . 99
M = 518 . 9 . 11 \(⋮\)9
Mình sửa lại để nha \(\left(125^7-625^5-25^9\right)\div99\)
Ta có \(\frac{\left(5^3\right)^7-\left(5^4\right)^6-\left(5^2\right)^9}{99}\)
\(=\frac{5^{21}-5^{20}-5^{18}}{99}\)
\(=\frac{5^{18}.\left(5^3-5^2-1\right)}{99}\)
\(=\frac{5^{18}.99}{99}\)
\(=5^{18}\)