bài 3
rút gọn biểu thức
\(A=\frac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}\)
\(B=\frac{\left(3.4.2^{16}\right)^{^2}}{11.2^{13}.4^{11}16^9}\)
1) 1.2.3...9 - 1.2.3...8 - 1.2.3...7.82
2) \(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)
3)13 - 12 + 11 + 10 - 9 + 8 - 7 - 6 + 5 -4 +3 +2 -1
Câu 1 dễ mà :
1.2.3...9 - 1.2.3...8 - 1.2.3...7.82
= 1.2.3...8.9 - 1.2.3...8.1 - 1.2.3...7.8.8
= 1.2.3...8.( 9 - 1 - 8 )
= 1.2.3...8.0
= 0
còn câu 2 và 3 thì sao
K ghi lại đề câu 2 nha :
\(=\frac{3^2.\left(2^2\right)^2.2^{32}}{11.2^{13}.\left(2^2\right)^{11}-\left(2^4\right)^9}\)
\(=\frac{3^2.2^4.2^{32}}{11.2^{13}.2^{22}-2^{36}}\)
\(=\frac{3^2.2^{36}}{11.2^{35}-2^{35}.2}\)
\(=\frac{3^2.2^{36}}{2^{35}\left(11-2\right)}\)
\(=\frac{3^2.2^{36}}{2^{35}.3^2}\)
\(=\frac{3^2}{3^2}.\frac{2^{36}}{2^{35}}\)
\(=1.2=2\)
thực hiện các phép tính sau một cách hợp lí:
a,\(\left(10^2+11^2+12^2\right):\left(13^2+14^2\right)\)
b,\(1.2.3...9-1.2.3...8-1.2.3...7.8^2\)
c,\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)
d,1152-(374+1152)+(-65+374)
e,13-12+11+10-9+8-7-6+5-4+3-2-1
a) =\(\left[\left(12+1\right)^2+\left(12+2\right)^2\right]:\left(13^2+14^2\right)\)
=1
b)=(1.2.3....8).(9-1-8)
=(1.2.3....8).0
=0
mik chỉ giải được zậy thôi.
t mik nha.
Tính các gtri các biểu thức sau :
a, A = \(\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
b,B=\(^{\frac{72^3.54^2}{108^4}}\)
c,C = \(\frac{11^{22}.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
d, D= \(\frac{\left(3.4.2^{16}\right)}{11.2^{13}.4^{11}-16^9}\)
a, A = \(\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
\(A=\frac{2^{10}\left(13+65\right)}{2^8.2^2.26}=\frac{2^{10}.78}{2^{10}.26}=\frac{78}{26}=3\)
Vậy A = 3
b, \(B=\frac{72^3.54^2}{108^4}=\frac{72^3.54^2}{\left(54.2\right)^4}=\frac{72^3.54^2}{54^4.2^4}=\frac{72^3}{54^2.2^4}=\frac{\left(8.9\right)^3}{\left(6.9\right)^2.2^4}\)
\(=\frac{\left(2^3\right)^3.9^3}{6^2.9^2.2^4}=\frac{2^9.9^3}{2^2.3^2.9^2.2^4}=\frac{2^9.9^3}{2^6.9^3}=\frac{2^9}{2^6}=2^3=8\)
Vậy B = 8
c, \(C=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=\frac{11.3^{29}.3^{30}}{2^2.3^{28}}=\frac{11.3^{29}.3.3^{29}}{2^2.3^{28}}=\frac{\left(11-3\right)3^{29}}{2^2.3^{28}}\)
\(=\frac{2^3.3^{29}}{2^2.3^{28}}=2.3=6\)
Vậy C = 6
d, \(D=\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}=\frac{\left(3.2^{18}\right)^2}{11.2^{35}-\left(2^4\right)^9}=\frac{3^2.2^{36}}{11.2^{35}-2^{36}}=\frac{3^2.2^{36}}{\left(11-2\right)2^{35}}=\frac{3^2.2}{9}=2\)
Vậy D = 2
Tính giá trị của các biểu thức:
a) ( 102 + 112 + 122 ) : ( 132 + 142 )
b) 9! - 8! - 7! . 82
c)\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)
Tính giá trị biểu thức A x B
\(A=\frac{\frac{3}{10}+\frac{1}{2}-\frac{1}{6}}{\frac{1}{9}-\frac{1}{5}-\frac{1}{3}}\) \(B=\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)
Tính giá trị của biểu thức:
\(\frac{\left(3.4.2^{16}\right)^{^2}}{11.2^{13}.4^{11}-16^9}\)
\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)
\(=\frac{3^2.4^2.2^{32}}{11.2^{13}.\left(2^2\right)^{11}-\left(2^4\right)^9}\)
\(=\frac{3^2.\left(2^2\right)^2.2^{32}}{11.2^{13}.2^{22}-2^{36}}\)
\(=\frac{3^2.2^4.2^{32}}{11.2^{35}-2^{36}}\)
\(=\frac{3^2.2^{36}}{2^{35}.\left(11-2\right)}\)
\(=\frac{3^2.2^{36}}{2^{35}.9}=2\)
\(\text{Thực hiện các phép tính sau một cách hợp lý:}\)
\(a\)) \(\left(10^2+11^2+12^2\right):\left(13^2+14^2\right)\)
\(b\)) \(1.2.3...9-1.2.3...8-1.2.3...7.8^2\)
\(c\)) \(\dfrac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)
\(d\)) \(1152-\left(374+1152\right)+\left(-65+374\right)\)
\(e\)) \(13-12+11+10-9+8-7-6+5-4+3+2-1\)
\(a,\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\) \(\frac{3}{2}.x-\left(\frac{4}{5}-2.x\right)=1\frac{3}{10}.\frac{3}{2}\)
a,tính
\(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)=?
b,tìm x, biết
\(\frac{3}{2}.x-\left(\frac{4}{5}-2.x\right)=1\frac{3}{10}:\frac{3}{2}\)
a) \(\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}=\frac{\left(3.2^2.2^{16}\right)^2}{11.2^{13}.\left(2^2\right)^{11}-\left(2^4\right)^9}\)
\(=\frac{\left(3.2^{18}\right)^2}{11.2^{13}.2^{22}-2^{36}}\)
\(=\frac{3^2.2^{36}}{11.2^{35}-2^{36}}\)
\(=\frac{9.2^{36}}{2^{35}.\left(11-2\right)}\)
\(=\frac{9.2^{36}}{2^{35}.9}=2\)
b) \(\frac{3}{2}.x-\left(\frac{4}{5}-2.x\right)=1\frac{3}{10}:\frac{3}{2}\)
\(\frac{3}{2}.x-\frac{4}{5}+2.x=\frac{13}{10}:\frac{3}{2}\)
\(\left(\frac{3}{2}.x+2.x\right)-\frac{4}{5}=\frac{13}{10}.\frac{2}{3}\)
\(x.\left(\frac{3}{2}+2\right)-\frac{4}{5}=\frac{13}{15}\)
\(x.\frac{7}{2}=\frac{13}{15}+\frac{4}{5}\)
\(x.\frac{5}{2}=\frac{13}{15}+\frac{12}{15}\)
\(x.\frac{7}{2}=\frac{25}{15}=\frac{5}{3}\)
\(x=\frac{5}{3}:\frac{7}{2}\)
\(x=\frac{5}{3}.\frac{2}{7}=\frac{10}{21}\)