\(A=\left(\dfrac{5.5^3}{125^2.49}\right)^{15}:\left(\dfrac{5^6}{434}\right)^7\)
1 Tínha \(\left(\dfrac{5.5^3}{5^2.49}\right)^{15}:\left(\dfrac{5^6}{434}\right)^7\)
b \(\dfrac{49^{24}.125^{10}.2^8-5^{30}.7^{49}.4^5}{5^{29}.16^2.7^{48}}\)
làm nhanh giúp mik nha, chiều mai phải nộp rồi...thanks bn giúp mik nhiều lắm lun !!!
a: \(=\left(\dfrac{5^4}{5^2\cdot7^2}\right)^{15}:\left(\dfrac{5^6}{2\cdot7\cdot31}\right)^7\)
\(=\dfrac{5^{30}}{7^{30}}:\dfrac{5^{42}}{2^7\cdot7^7\cdot31^7}\)
\(=\dfrac{5^{30}}{7^{30}}\cdot\dfrac{2^7\cdot7^7\cdot31^7}{5^{42}}=\dfrac{2^7\cdot31^7}{7^{23}\cdot5^{12}}\)
b: \(=\dfrac{7^{48}\cdot5^{30}\cdot2^8-5^{30}\cdot7^{49}\cdot2^{10}}{5^{29}\cdot2^8\cdot7^{48}}\)
\(=\dfrac{7^{48}\cdot5^{30}\cdot2^8\left(1-7\cdot4\right)}{5^{29}\cdot2^8\cdot7^{48}}=5\cdot\left(-27\right)=-135\)
1. \(25\dfrac{1}{7}:\left(-\dfrac{5}{7}\right)-15\dfrac{1}{7}:\left(-\dfrac{5}{7}\right)+\dfrac{4}{5}\) 3. \(2\dfrac{2}{3}:\left\{\left[\left(3,72-0.02\right)\dfrac{10}{37}\right]:\dfrac{5}{6}+2,8\right\}-\dfrac{7}{15}\)
2. \(\left(3+\dfrac{4}{5}-\dfrac{5}{12}\right)\left(\dfrac{6}{7}-\dfrac{3}{5}\right)^2\)
4.23+3.\(\left(-\dfrac{1}{2}\right)^2\)-22.4+\(\left[\left(-2\right)^2:\dfrac{1}{2}\right]\)
2: \(=\dfrac{203}{60}\cdot\dfrac{81}{1225}=\dfrac{783}{3500}\)
tính giá trị biểu thức sau
a) \(A=\dfrac{25^6}{5^3}\)
b) \(B=32.\left(\dfrac{3}{2}\right)^5\)
c) \(C=\left(\dfrac{1}{3}\right)^4.3^{-3}\)
d) \(D=4^{-2}.\left(\dfrac{2}{5}\right)^5.5^4\)
e) \(E=9^{-5}:\left(\dfrac{5}{3}\right)^4.25^2\)
f) \(F=\left(\dfrac{5}{8}\right)^{-2}:4^2\)
g) \(G=\left(\dfrac{5}{3}\right)^3.\left(\dfrac{9}{2}\right)^2:\left(\sqrt{3}\right)^4\)
a: \(A=\dfrac{25^6}{5^3}=\dfrac{\left(5^2\right)^6}{5^3}=\dfrac{5^{12}}{5^3}=5^9\)
b: \(B=32\cdot\left(\dfrac{3}{2}\right)^5=32\cdot\dfrac{3^5}{2^5}=32\cdot\dfrac{243}{32}=243\)
c: \(C=\left(\dfrac{1}{3}\right)^4\cdot3^{-3}=3^{-4}\cdot3^{-3}=3^{-4-3}=3^{-7}\)
d: \(D=4^{-2}\cdot\left(\dfrac{2}{5}\right)^5\cdot5^4\)
\(=\dfrac{1}{4^2}\cdot\dfrac{2^5}{5^5}\cdot5^4\)
\(=\dfrac{1}{16}\cdot\dfrac{32}{5}=\dfrac{2}{5}\)
e: \(E=9^{-5}:\left(\dfrac{5}{3}\right)^4\cdot25^2\)
\(=\dfrac{1}{9^5}:\dfrac{5^4}{3^4}\cdot\left(5^2\right)^2\)
\(=\dfrac{1}{3^{10}}\cdot\dfrac{3^4}{5^4}\cdot5^4=\dfrac{1}{3^6}\)
f: \(F=\left(\dfrac{5}{8}\right)^{-2}:4^2\)
\(=\left(1:\dfrac{5}{8}\right)^2:4^2\)
\(=\left(\dfrac{8}{5}\right)^2\cdot\dfrac{1}{16}=\dfrac{64}{25}\cdot\dfrac{1}{16}=\dfrac{4}{25}\)
g: \(G=\left(\dfrac{5}{3}\right)^3\cdot\left(\dfrac{9}{2}\right)^2:\left(\sqrt{3}\right)^4\)
\(=\dfrac{5^3}{3^3}\cdot\dfrac{9^2}{2^2}:9\)
\(=\dfrac{5^3\cdot3^4}{3^3\cdot2^2}\cdot\dfrac{1}{3^2}\)
\(=\dfrac{125}{2^2\cdot3}=\dfrac{125}{3\cdot4}=\dfrac{125}{12}\)
\(A=\dfrac{\left(5^2\right)^6}{5^3}=\dfrac{5^{12}}{5^3}=5^9\)
\(B=32.\left(\dfrac{3}{2}\right)^5=\dfrac{2^5.3^5}{2^5}=2^5\)
\(C=\left(\dfrac{1}{3}\right)^4.3^{-3}=\dfrac{1}{3^4.3^3}=\dfrac{1}{3^7}\)
\(D=4^{-2}.\left(\dfrac{2}{5}\right)^5.5^4=\dfrac{1}{\left(2^2\right)^2}.\dfrac{2^5}{5^5}.5^4=\dfrac{2}{5}\)
\(E=\dfrac{1}{9^5}.\dfrac{3^4}{5^4}.\left(5^2\right)^2=\dfrac{1}{3^{10}}.\dfrac{3^4}{5^4}.5^4=\dfrac{1}{3^6}\)
\(F=\dfrac{8^2}{5^2}:\left(2^2\right)^2=\dfrac{\left(2^3\right)^2}{5^2.2^4}=\dfrac{2^6}{5^2.2^4}=\dfrac{2^2}{5^2}\)
\(G=\dfrac{5^3}{3^3}.\dfrac{\left(3^2\right)^2}{2^2}:3^2=\dfrac{5^3}{3^3}.\dfrac{3^4}{2^2}.\dfrac{1}{3^2}=\dfrac{5^3}{3.2^2}\)
A=\(\left[\dfrac{1\dfrac{11}{31}.4\dfrac{3}{7}-\left(15-6\dfrac{1}{3}.\dfrac{2}{19}\right)}{4\dfrac{5}{6}+\dfrac{1}{6}\left(12-5\dfrac{1}{3}\right)}.\left(-1\dfrac{14}{93}\right)\right].\dfrac{31}{50}\)
giải phương trình
a) \(6^x=5\)
b) \(7^{3-x}=5\)
c) \(\left(\dfrac{3}{5}\right)^{x-2}=\dfrac{27}{125}\)
d) \(\left(\dfrac{4}{5}\right)^x=\dfrac{5}{4}\)
a: \(6^x=5\)
=>\(x=log_65\)
b: \(7^{3-x}=5\)
=>\(3-x=log_75\)
=>\(x=3-log_75\)
c: \(\left(\dfrac{3}{5}\right)^{x-2}=\dfrac{27}{125}\)
=>\(\left(\dfrac{3}{5}\right)^{x-2}=\left(\dfrac{3}{5}\right)^3\)
=>x-2=3
=>x=5
d: \(\left(\dfrac{4}{5}\right)^x=\dfrac{5}{4}\)
=>\(\left(\dfrac{4}{5}\right)^x=\left(\dfrac{4}{5}\right)^{-1}\)
=>x=-1
a.
\(6^x=5\Rightarrow x=log_65\)
b.
\(7^{3-x}=5\Rightarrow3-x=log_75\)
\(\Rightarrow x=3-log_75\)
c.
\(\left(\dfrac{3}{5}\right)^{x-2}=\dfrac{27}{125}\Rightarrow x-2=log_{\dfrac{3}{5}}\left(\dfrac{27}{125}\right)\)
\(\Rightarrow x-2=3\Rightarrow x=5\)
d.
\(\left(\dfrac{4}{5}\right)^x=\dfrac{5}{4}\Rightarrow\left(\dfrac{4}{5}\right)^x=\left(\dfrac{4}{5}\right)^{-1}\)
\(\Rightarrow x=-1\)
\(\left(\dfrac{2}{3}-\dfrac{1}{2}-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}-\dfrac{1}{7}\right)\)
\(\left(\dfrac{15}{21}:\dfrac{5}{7}\right):\left(\dfrac{6}{5}:2\right)\)
a) \(\left(\dfrac{2}{3}-\dfrac{1}{2}-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}-\dfrac{1}{7}\right)\)
\(=-\dfrac{1}{6}\cdot\dfrac{17}{28}\)
\(=-\dfrac{17}{168}\)
b) \(\left(\dfrac{15}{21}\div\dfrac{5}{7}\right)\div\left(\dfrac{6}{5}\div2\right)\)
\(=1\div\dfrac{3}{5}\)
\(=\dfrac{5}{3}\)
(2/3 - 1/2 - 1/3) . (1-1/4 - 1/7)
= -1/6 . 17/28
= -17/168
(15/21 : 5/7 ) : (6/5 : 2)
= 1 : 3/5
= 5/3
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) \(\dfrac{45^{10}.5^{20}}{75^{15}}\)
a, \(125^3:5^7=\left(5^3\right)^3:5^7=5^9:5^7=5^2\)
b, \(\left(\dfrac{2}{7}\right)^{18}:\left(\dfrac{4}{49}\right)^5:\left(\dfrac{8}{343}\right)^2\)
= \(\left(\dfrac{2}{7}\right)^{18}:\left(\dfrac{2^2}{7^2}\right)^5:\left(\dfrac{2^3}{7^3}\right)^2\)
= \(\left(\dfrac{2}{7}\right)^{18}:\left[\left(\dfrac{2}{7}\right)^2\right]^5:\left[\left(\dfrac{2}{7}\right)^3\right]^2\)
=\(\left(\dfrac{2}{7}\right)^{18}:\left(\dfrac{2}{7}\right)^{10}:\left(\dfrac{2}{7}\right)^6\)
= \(\left(\dfrac{2}{7}\right)^{18-10-6}=\left(\dfrac{2}{7}\right)^2\)
c, \(3-\left(\dfrac{-7}{9}\right)^0+\left(\dfrac{1}{3}\right)^5.3^5\)
= 3 - 1 +\(\left[\left(\dfrac{1}{3}\right)^5.3^5\right]\)
= 2 + 1=3
d, \(\dfrac{45^{10}.5^{20}}{75^{15}}=\dfrac{\left(9.5\right)^{10}.5^{20}}{\left(25.3\right)^{15}}=\dfrac{\left(3^2\right)^{10}.5^{10}.5^{20}}{\left(5^2\right)^{15}.3^{15}}\)
= \(\dfrac{3^{20}.5^{30}}{5^{30}.3^{15}}=3^5\)
a) Tính A = 1 - 2 + 22 - 23 +...+ 2100
b) B = \(\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^2.49^2}{\left(125.7\right)^3+5^9.14^3}\)
hãy tính giá trị của biểu thức sau:
C=\(\left|-3\left(-\dfrac{13}{15}-\dfrac{17}{21}\right)\right|-\left|-\dfrac{13}{5}+\dfrac{17}{7}\right|+\left(-12+\dfrac{35}{3}\right):\left|-\dfrac{7}{6}\right|\)
\(C=\left|-3\left(\dfrac{-13}{15}-\dfrac{17}{21}\right)\right|-\left|\dfrac{-13}{15}+\dfrac{17}{7}\right|+\left(-12+\dfrac{35}{3}\right):\left|-\dfrac{7}{6}\right|\\ =\left|-3.-\dfrac{176}{105}\right|-\left|-\dfrac{6}{35}\right|+\left(-\dfrac{1}{3}\right):\dfrac{7}{6}\\ =\dfrac{176}{35}-\dfrac{6}{35}-\dfrac{1}{3}:\dfrac{7}{6}\\ =\dfrac{176}{35}-\dfrac{6}{35}-\dfrac{2}{7}\\ =\dfrac{170}{35}-\dfrac{2}{7}=\dfrac{32}{7}.\)