Hãy so sánh B và C: \(B=\frac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}\) và \(C=\frac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}\)
Rút gọn biểu thức:
\(\frac{2^{12}\cdot13+2^{12}\cdot65}{2^{10}\cdot104}+\frac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}\)
\(\frac{2^{12}.13+2^{12}.65}{2^{10}.104}+\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
\(\Rightarrow\frac{2^{12}.\left(13+65\right)}{2^{10}.104}+\frac{3^{10}.\left(11+5\right)}{3^9.2^4}\)
\(\Rightarrow\frac{2^{12}.78}{2^{10}.104}+\frac{3^{10}.2^4}{3^9.2^4}\)
\(=\frac{2^2.3}{4}+3\)
\(=3+3=6\)
Bài 22 : a, Cho A = 4 + 22 + 23 + 24 + ... + 220
Hỏi A có chia hết cho 128 không ?
b, Tính giá trị biểu thức
\(\frac{2^{12}\cdot13+2^{12}\cdot65}{2^{10}\cdot104}+\frac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}\)
b)
\(\frac{2^{12}.13+2^{12}.65}{2^{10}.104}+\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
\(=\frac{2^{10}\left(4.13+4.65\right)}{2^{10}.104}+\frac{3^9\left(11.3+5.3\right)}{3^9.16}\)
\(=\frac{312}{104}+\frac{48}{16}=3+3=6\)
a) \(A=4+2^2+2^3+2^4+....+2^{20}\)
\(\Rightarrow2A=2^3+2^3+2^4+.....+2^{21}\)
\(\Rightarrow2A-A=\left(2^3+2^3+2^4+....+2^{21}\right)-\left(2^2+2^3+2^4+...+2^{20}\right)\)
\(\Rightarrow A=2^3+2^{21}-\left(2^2+2^2\right)\)
\(\Rightarrow A=2^{21}\)
\(\text{Vì }2^{21}⋮2^7\Rightarrow A⋮128\)
b) \(\frac{2^{12}.13+2^{12}.65}{2^{10}.104}+\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
\(=\frac{2^{12}\left(13+65\right)}{2^{10}.2^3.13}+\frac{3^{10}\left(11+5\right)}{3^9.2^4}\)
\(=\frac{2^{12}.78}{2^{13}.13}+\frac{3^{10}.16}{3^9.16}=\frac{6}{2}+\frac{3^{10}}{3^9}\)
\(=3+3=6\)
b\(^{\frac{2^{10\cdot13+2^{10}\cdot65}}{2^8\cdot104}}\)
c) \(\frac{5\cdot4^{15}-99-4\cdot3^{20}\cdot89}{5\cdot29\cdot6^{19}\cdot7\cdot2^{29}\cdot27^6}\)
b\(^{\frac{2^{10\cdot13+2^{10}\cdot65}}{2^8\cdot104}}\)
c) \(\frac{5\cdot4^{15}-99-4\cdot3^{20}\cdot89}{5\cdot29\cdot6^{19}\cdot7\cdot2^{29}\cdot27^6}\)
Tính gíá trị biểu thức :
A= \(\frac{3^{10}\cdot11+\left(3^2\right)^5:5}{24\cdot27}\)
B= \(\frac{2^{10}\cdot13+2^{10}\cdot65}{28\cdot104}\)
AI NHANH MK K CHO
cách làm :
câu B
ta thấy có 2 lần 210 xuất hiện trên 1 phần tử
ta gộp lại như sau :
210 x ( 13 + 65 ) cho dễ
còn câu A
ta không thể tóm gọn nên phải tính như bình thường
A = 649539 + 45 / 648
A = 1002 . 44444444444444444
hay 649584 / 648
B = 0 + 66560 / 2912
B = 22 . 8571428571
hay 66560 / 2912
Đ/s : .........
nhé !
cho mình sửa lại câu B
B = 1024 x ( 13 + 65 ) / 2912
B = 79872 / 2912
a,\(A=\frac{3^{10}\cdot11+\left(3^2\right)^5:5}{27\cdot24}\)
b, \(B=\frac{2^{10}+13+2^{10}\cdot65}{28\cdot104}\)
A = \(\frac{72^3\cdot54^2}{108^4}\)
B = \(\frac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}\)
\(A=\frac{72^3\times54^2}{108^4}=\frac{\left(2^3\times3^2\right)^3\times\left(2\times3^3\right)^2}{\left(2^2\times3^3\right)^4}=\frac{2^9\times3^6\times2^2\times3^6}{2^8\times3^{12}}=2^3=8\)
\(B=\frac{3^{10}\times11+3^{10}\times5}{3^9\times2^4}=\frac{3^{10}\times\left(11+5\right)}{3^9\times16}=\frac{3\times16}{16}=3\)
Chúc bạn học tốt
a) \(\frac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}\)
b) (1+2+3+4+....+100)x(\(1^2\) +\(2^2\) \(3^2\) +....+\(10^2\) )x(65 x 111 -13x15x37)
a.
\(\frac{2^{10}\times13+2^{10}\times65}{2^8\times104}=\frac{2^{10}\times\left(13+65\right)}{2^8\times104}=\frac{2^2\times78}{104}=\frac{4\times78}{104}=\frac{312}{104}=3\)
b.
\(\left(1+2+...+100\right)\times\left(1^2+2^2+...+10^2\right)\times\left(65\times111-15\times37\times13\right)\)
\(=\left(1+2+...+100\right)\times\left(1^2+2^2+...+10^2\right)\times\left(7215-7215\right)\)
\(=\left(1+2+...+100\right)\times\left(1^2+2^2+...+10^2\right)\times0\)
= 0
\(\frac{2^{13}+2^5}{2^{10}+2^2}\)
\(\frac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}\)
\(\frac{2^{13}+2^5}{2^{10}+2^2}=\frac{2^5.\left(2^8+1\right)}{2^2.\left(2^8+1\right)}=2^3=8\)
\(\frac{2^{10}.13+2^{10}.65}{2^8.104}=\frac{2^{10}.\left(13+65\right)}{2^8.104}=\frac{2^2.78}{104}=3\)