Bài3Tính giá trị biểu thức
a) A=\(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
b) B=\(\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
c) C=\(\frac{72^3.54^2}{108^4}\)
d) D=\(\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
A=\(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
B=\(\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
C=\(\frac{72^3.54^2}{108^4}\)
D=\(\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
Gợi ý
bn thực hiện phép tính tử mẫu bình thường , khi ra nhưng số trùng nhau bn gạch ra nháp cho đến nhưng số tối giản là ra nha
chúc bn
học tốt
A = \(\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
= \(\frac{3^{10}\left(11+5\right)}{3^9.2^4}\)
= \(\frac{3^{10}.16}{3^9.2^4}\)
= \(\frac{3^{10}.2^4}{3^9.2^4}=3\)
B = \(\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
= \(\frac{2^{10}\left(13+65\right)}{2^8.104}\)
= \(\frac{2^{10}.78}{2^8.104}\)
= \(\frac{2^{10}.13.2.3}{2^8.2^3.13}\)
= \(\frac{2^{11}.13.3}{2^{11}.13}=3\)
C = \(\frac{72^3.54^2}{108^4}\)
= \(\frac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}\)
= \(\frac{2^9.3^6.2^2.3^6}{2^8.3^{12}}\)
= \(\frac{2^{11}.3^{12}}{2^8.3^{12}}\)
= \(2^3=8\)
\(A=\frac{3^{10}.11.3^{10}}{^{ }3^9.2^4}\)
\(B=\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
\(C=\frac{72^3.54^2}{108^4}\)
\(D=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
Tính giá trị các biểu thức
A=\(\frac{3^{10\ \ }.11+3^{10\ \ }.5}{3^{9\ }.2^{^4}\ }\)
B= \(\frac{2^{10}.13+2^{10\ }.65}{2^8.104}\)
C=\(\frac{72^3.54^2}{108^4}\)
D=\(\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
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
A=\(\dfrac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
B=\(\dfrac{2^{10}.13+2^{10}.65}{2^8.104}\)
C=\(\dfrac{72^3.54^2}{108^4}\)
D=\(\dfrac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
\(A=\dfrac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}=\dfrac{3^{10}\cdot\left(11+5\right)}{3^9\cdot16}=\dfrac{3^{10}\cdot16}{3^9\cdot16}=3\)
\(B=\dfrac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}=\dfrac{2^{10}\cdot\left(13+65\right)}{2^8\cdot2^2\cdot26}=\dfrac{2^{10}\cdot78}{2^{10}\cdot26}=3\)
\(C=\dfrac{72^3\cdot54^2}{108^4}=\dfrac{\left(2^3\cdot3^2\right)^3\cdot\left(2\cdot3^3\right)^2}{\left(3^3\cdot2^2\right)^4}\\ =\dfrac{2^9\cdot3^6\cdot2^4\cdot3^6}{3^{12}\cdot2^8}=\dfrac{2^{13}\cdot3^{12}}{3^{12}\cdot2^8}=2^5=32\)
\(D=\dfrac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}=\dfrac{11\cdot3^{29}-\left(3^2\right)^{15}}{2^2\cdot3^{28}}=\dfrac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}\\ =\dfrac{3^{29}\cdot\left(11-3\right)}{2^2\cdot3^{28}}=\dfrac{3^{29}\cdot8}{4\cdot3^{28}}=3\cdot2=6\)
Tính giá trị của các biểu thức :
a , A = \(\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
b , B = \(\frac{4^9.36+64^4}{16^4.100}\)
c , C = \(\frac{72^3.54^2}{108^4}\)
d , D = \(\frac{4^6.3^4.9^5}{6^{12}}\)
e , E = \(\frac{2^{13}+2^5}{2^{10}+2^2}\)
f , F = \(\frac{21^2.14.125}{35^5.6}\)
g , G = \(\frac{45^3.20^4.18^2}{180^5}\)
h , H = \(\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
mấy bn lm giúp mk nha , mk tk cho 3 tk
35) Tính giá trị của các biểu thức
\(A=\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
\(B=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
Bài 35 :
\(A=\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
\(A=\frac{2^{10}.\left(13+65\right)}{2^8.104}\)
\(A=\frac{2^8.2^2.98}{2^8.104}\)
\(A=\frac{2^8.4.98}{2^8.4.26}\)
\(A=\frac{49}{13}\)
Vậy \(A=\frac{49}{13}\)
\(B=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
\(B=\frac{11.3^{29}-9^{15}}{2^2.\left(3^{14}\right)^2}\)
\(B=\frac{11.3^{29}-9^{15}}{2^2.3^{28}}\)
\(B=\frac{11.3^{29}-\left(3^2\right)^{15}}{4.3^{28}}\)
\(B=\frac{11.3^{29}-3^{30}}{4.3^{28}}\)
\(B=\frac{11.3^{29}-3^{29}.3}{4.3^{28}}\)
\(B=\frac{3^{29}.\left(11-3\right)}{4.3^{28}}\)
\(B=\frac{3^{29}.8}{4.3^{28}}\)
\(B=\frac{3^{28}.3.4.2}{4.3^{28}}\)
\(B=3.2\)
\(B=6\)
Vậy B = 6
A = 2^10 . 13 + 2^10 . 65 / 2^8 . 104
= 2^10 ( 13 + 65 ) / 2^8 . 104 = 2^10 . 78 / 2^8 . 104 = 2^8 . 2^2 . 78 / 2^8 . 104 = 2^8 . 4 . 78 / 2^8 . 104 = 2^8 . 312 / 2^8 . 104
= 312/104
= 3
B = 11 . 3^22 . 3^7 - 9^15 / ( 2.3^14)^2
= 11 . 3^29 - (3^2)^15 / ( 3.2^14)^2
= 11 . 3^29 - 3^30 / ( 3. 2 )^28
= ( 8 + 3 ) . 3^29 - 3^30 / ( 3. 2)^28
= 8 . 3^29 + 3.3^29 - 3^30 / ( 3.2)^28
= 8 . 3^29 + 3^30 - 3^30 / ( 3 . 2)^28
= 8 . 3^29 / 3^28 . 2^28
= 2^3 . 3 / 2^28
= 3/ 2^25
Rút gọn:
A= \(\frac{72^3.54^2}{1084}\) ; B= \(\frac{3^{10}+11+3^{10}.5}{3^9.2^4}\) ; C= \(\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
\(A=\frac{72^2.54^2}{1084}=\frac{\left(72.54\right)^2}{1084}=\frac{3888^2}{1084}=\frac{3888.3888}{1084}=\frac{972.3888}{271}=\frac{3779136}{271}\)
Tính giá trị các biểu thức
a, A= 3^10.11+3^10.5 / 3^9.2^4
b, B= 2^10.13+2^10.65 / 2^8.104
c, C= 72^3.54^2 / 108^4
d, D= 11.3^22.3^7-9^15 / ( 2.3^14)^2
\(A=\frac{3^{10}.11+3^{10}.5}{3^9.2^4}=\frac{3^{10}.16}{3^9.16}=3\)
\(B=\frac{2^{10}.13+2^{10}.65}{2^8.104}=\frac{2^{10}.78}{2^8.104}=\frac{2^{10}.26.3}{2^8.2^2.26}=3\)
\(C=\frac{72^3.52^4}{108^4}=\frac{\left(3^2.2^3\right)^3.\left(13.2^2\right)^4}{\left(3^3.2^2\right)^4}=\frac{3^6.2^9.13^4.2^8}{3^{12}.2^8}=\frac{2^9.13^4}{3^6}\)
\(D=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=\frac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}=\frac{11.3^{29}-3^{30}}{2^2.3^{28}}=\frac{3^{29}\left(33-1\right)}{2^2.3^{28}}=\frac{3^{29}.2^5}{2^2.3^{28}}=3.8=24\)