\(\dfrac{45^{10}.5^{20}}{75^{15}}=\dfrac{\left(3^2\right)^{10}.5^{10}.5^{20}}{\left(5^2\right)^{15}.3^{15}}\dfrac{3^{20}.5^{30}}{5^{30}.3^{15}}=3^5\)
\(\dfrac{2^{15}.9^4}{6^6.8^3}=\dfrac{2^{15}.\left(3^2\right)^4}{2^3.3^3.\left(2^3\right)^3}=\dfrac{2^{15}.3^8}{2^3.3^3.2^9}=\dfrac{2^{15}.3^8}{2^{12}.3^3}\) =\(2^3.8^5\)
1.Tính :
a) 1253 : 57
b) \(\left(\dfrac{2}{7}\right)^{18}:\left(\dfrac{4}{49}\right)^5:\left(\dfrac{8}{343}\right)^2\)
c) 3 - \(\left(-\dfrac{7}{9}\right)^0+\left(\dfrac{1}{3}\right)^5.3^5\)
d) \(\dfrac{45^{10}.5^{20}}{75^{15}}\)
\(\dfrac{45^{10}.5^{20}}{75^{15}}\)
Tính:
N = \(\dfrac{6^6+6^3.3^3+3^6}{-73}\)
T= \(\dfrac{45^{10}.5^{10}}{75^{15}}\)
tìm giá trị của các biểu thức sau
a) \(\dfrac{45^{10}.5^{20}}{75^{15}}\)
b) \(\dfrac{\left(0,8\right)^5}{\left(0,4\right)^6}\)
Tìm x, biết rằng:
1) ( 2x + 1)3 = -0,001
2) ( 2x -3 )4 = ( 2x-3 )6
3) ( 2x+1 )5 = ( 2x+1)2010
4) \(\dfrac{8}{25}=\dfrac{2^x}{5^{x-1}}\)
5) 9x : 3x = 3
6) \(3^x+3^{x+3}=756\)
7) \(5^{x+1}+6.5^{x+1}=875\)
8) \(2^{x-1}.3^{y+1}=12^{x+9}\)
9) \(3^x=9^{y-1}\)
10) \(2^{x+1}.5^y=20^x\)
11) 15x : 3y = 75y
12) \(\dfrac{3}{5}:\dfrac{2x}{15}=\dfrac{1}{2}:\dfrac{4}{5}\)
13) \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\) và xy + yz + zx = 104
Tinh
\(\dfrac{\left(1+2+3+...+100\right)\left(\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{7}-\dfrac{1}{9}\right)\left(6,3.12-21.36\right)}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}}\)
\(\dfrac{\left(\dfrac{3}{10}-\dfrac{4}{15}-\dfrac{7}{20}\right).\dfrac{5}{9}}{\left(\dfrac{1}{14}+\dfrac{1}{7}-\dfrac{-3}{35}\right)\dfrac{-4}{3}}\)
Tìm x,y,z trong dãy tỉ số bằng nhau
1)\(\dfrac{3x}{8}=\dfrac{3y}{64}=\dfrac{3z}{216}\)và \(2x^2+2y^2.z^2=1\)
2) \(\dfrac{2x+1}{5}=\dfrac{4y-5}{9}=\dfrac{2x+4y-4}{7x}\)
3) \(\dfrac{x^3+y^3}{6}=\dfrac{x^3-2y^3}{4}\)và x6 . y6 =14
4) \(\dfrac{x+4}{6}=\dfrac{3y-1}{8}=\dfrac{3y-x-5}{x}\)
5) \(\dfrac{3}{x-1}=\dfrac{4}{y-2}=\dfrac{5}{z-3}\)và x.y.z=192
6)\(\dfrac{x-y}{3}=\dfrac{x+y}{13}=\dfrac{x.y}{200}\)
7)\(\dfrac{x+1}{2}=\dfrac{y-1}{3}=\dfrac{z+2}{4}=\dfrac{x+y+z+2}{2x+5}\)
8) \(\dfrac{15}{x-9}=\dfrac{20}{y-12}=\dfrac{40}{z-24}\)và x.y = 1200
9)\(\dfrac{40}{x-30}=\dfrac{20}{y-15}=\dfrac{28}{z-21}\) và x.y.z = 22400
10)15x = -10y =6z và x.y.z = -30000
11) Cho\(\dfrac{x+1}{3}=\dfrac{y-2}{5}=\dfrac{2z+14}{9}\)và x+z=y
12) Cho \(\dfrac{x}{3}=\dfrac{y}{4}\)và \(\dfrac{y}{5}=\dfrac{z}{6}\).Tính M=\(\dfrac{2x+3y+4z}{3x+4y+5z}\)
tính nhanh
\(\dfrac{3^6.45^4-15^{13}:5^9}{27^4.25^3+45^6}\)
tính hợp lý \(\dfrac{3^{^{^{ }}6}.45^5-15^{13}:5^9}{27^4.25^3+45^6}\)
