Tính nhanh :
\(125\times2^3-\left(27-33\right)+ \left(15-29+8\right)\times2015^0\)
bài 6: tính :
\(\dfrac{10^9.\left(-81\right)^{10}}{\left(-8\right)^4.25^5.9^{10}}\)
b,\(\dfrac{9^4.\left(-4\right)^5.25^3}{8^3,\left(-27\right)^2.5^7}\)
c,\(\dfrac{3^{186}.\left(-25\right)^{50}}{\left(-15\right)^{100}.27^{29}}\)
a: \(=\dfrac{2^9\cdot5^9\cdot3^{40}}{2^{12}\cdot5^{10}\cdot3^{20}}=\dfrac{3^{20}}{5\cdot2^3}\)
b: \(=\dfrac{-3^8\cdot2^{10}\cdot5^6}{2^9\cdot\left(-1\right)\cdot3^6\cdot5^7}=\dfrac{-2}{5}\cdot3^2=-\dfrac{18}{5}\)
c: \(=\dfrac{3^{186}\cdot5^{100}}{5^{100}\cdot3^{187}}=\dfrac{1}{3}\)
1) tính
a)\(\dfrac{27^{15}\times5^3\times8^4}{25^2\times81^{11}\times2^{11}}\)
b)\(\left(\dfrac{1}{25}-0,6\right)^2\div\dfrac{49}{125}+[\left(3\dfrac{1}{4}-6\dfrac{5}{9}\right)\times2\dfrac{2}{17}]\)
c)\(|1-\dfrac{2}{3}|-2\times\left(\dfrac{-209}{2009}\right)^0\)
a,
\(\dfrac{\left(3^3\right)^{15}.5^3.\left(2^3\right)^4}{\left(5^2\right)^2.\left(3^4\right)^{11}.2^{11}}=\dfrac{3^{45}.5^3.2^{12}}{5^4.3^{44}.2^{11}}=\dfrac{6}{5}\)
b, \(\left(-\dfrac{14}{25}\right)^2.\dfrac{125}{49}+\left(-3\dfrac{11}{36}\right).2\dfrac{2}{17}=\dfrac{4}{5}.\left(-7\right)=-\dfrac{28}{5}\)
c, \(\dfrac{1}{3}-2.1=-\dfrac{5}{3}\)
Giải phương trình sau;
a) \(125x^3-\left(2x+1\right)^3-\left(3x-1\right)^3=0\)
b) \(\left(x-1\right)^3+\left(x+1\right)^3=8\left(x-1\right)^3\)
c) \(\frac{x+19}{27}+\frac{x+17}{29}=\frac{x+15}{31}-\frac{x+13}{33}\)
Giải các phương trình sau:
a) \(125x^3-\left(2x+1\right)^3-\left(3x-1\right)^3=0\)
b) \(\left(x-1\right)^3+\left(x+1\right)^3=8\left(x-1\right)^3\)
c)\(\frac{x+19}{27}+\frac{x+17}{29}=\frac{x+15}{31}-\frac{x+13}{33}\)
\(-29\times165+29\times65\)
\(\left\{215-\left[5\times(5\times16-25\times2)-\right]60\right\}\div5^3\)
tính hợp lí
\(-29\times165+29\times65=29\times\left(65-165\right)=29\times\left(-100\right)=-2900\\ ---\\ \left\{215-\left[5\times\left(5\times16-25\times2\right)\right]-60\right\}:5^3\\ =\left\{215-\left[5\times\left(80-50\right)\right]-60\right\}:125\\ =\left\{215-\left[5\times30\right]-60\right\}:125\\ =\left\{215-150-60\right\}:125=5:125=\dfrac{1}{25}\)
Giải phương trình sau:
a) \(125x^3-\left(2x+1\right)^3-\left(3x-1\right)^3=0\) \(\)
b) \(\left(x-1\right)^3+\left(x+1\right)^3=8\left(x-1\right)^3\)
c) \(\frac{x+19}{27}+\frac{x+17}{29}=\frac{x+15}{31}-\frac{x+13}{33}\)
Câu 2: K - 2013 = \(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+2015\right)}{2015\times1+2014\times2+2013\times3+...+2\times2014+1\times2015}\)
Tìm K
Tính S = \(\frac{5\times2^{30}\times6^2\times3^{15}-2^3\times8^9\times3^{17}\times21}{21\times2^{29}\times3^{16}\times4-2^{29}\times\left(3^4\right)^5}\)
Ta có : S = \(\frac{5.2^{30}.6^3.3^{15}-2^3.8^9.3^{17}.21}{21.2^{29}.3^{16}.4-2^{29}.\left(3^4\right)^5}=\frac{5.2^{30}.\left(2.3\right)^3.3^{15}-2^3.\left(2^3\right)^9.3^{17}.3.7}{3.7.2^{29}.3^{16}.2^2-2^{29}.3^{20}}=\frac{5.2^{33}.3^{18}-2^{30}.3^{18}.7}{3^{17}.7.2^{31}-2^{29}.3^{20}}\)
\(=\frac{2^{30}.3^{18}.\left(5.2^3-7\right)}{3^{17}.2^{29}.\left(7.2^2-3^3\right)}=2.3.33=198\)
Tính nhanh : \(\frac{1}{8}\div12,5\%+\left(\frac{1\times2\times3+6\times4\times2}{5\times3\times1+5\times15\times25}+\frac{1}{2}\div50\%\right)-\left(\frac{1}{16}\div6,25\%+\frac{3+2+1+2+4+6}{1+3+5+25+15+5}\right)-\frac{1}{4}\div25\%\)
\(\frac{1}{8}=12,5\%\) ; \(\frac{1}{16}=6,25\%\) ; \(\frac{1}{2}=50\%\) ; \(\frac{1}{4}=25\%\)
Thay vào trên mà tính.
= \(1+\left(\frac{3\left(1x2+2x4x2\right)}{3\left(5+5x3x25\right)}+1\right)-\left(1+\frac{18}{54}\right)-1\) = \(\frac{18}{380}-\frac{18}{54}\)