Tính \(\frac{5\times\left(2^2\times3^2\right)^9-\left(2^2\right)^6-2\left(2^2\times3\right)^{14}\times3^4}{5\times2^{28}\times3^{18}-2^{29}\times3^{18}}\)
TÍNH NHANH :
\(\frac{5\times\left(2^2\times3^2\right)^9-2\times\left(2^2\times3\right)^{14}\times3^4}{5\times2^{28}\times3^{18}-7\times2^{29}\times3^{18}}\)
A=\(\frac{5x\left(2^2x3^2\right)^9-2x\left(2^2x3\right)^{14}x3^4}{5x2^{28}x3^{18}-7x2^{29}x3^{18}}\)=\(\frac{5x2^{18}x3^{18}-2x2^{28}x3^{14}x3^4}{2^{28}x3^{18}x\left(5-7x2\right)}\)=\(\frac{5x2^{18}x3^{18}-2^{29}x3^{18}}{2^{28}x3^{18}x\left(-9\right)}\)=
= \(\frac{2^{18}x3^{18}\left(5-2^{11}\right)}{-9x2^{28}x3^{18}}=\frac{5-2^{11}}{-9x2^{10}}=\frac{2043}{9216}=\frac{227}{1024}\)
Tính S = \(\frac{5\times2^{30}\times6^2\times3^{15}-2^3\times8^9\times3^{17}\times21}{21\times2^{29}\times3^{16}\times4-2^{29}\times\left(3^4\right)^5}\)
Ta có : S = \(\frac{5.2^{30}.6^3.3^{15}-2^3.8^9.3^{17}.21}{21.2^{29}.3^{16}.4-2^{29}.\left(3^4\right)^5}=\frac{5.2^{30}.\left(2.3\right)^3.3^{15}-2^3.\left(2^3\right)^9.3^{17}.3.7}{3.7.2^{29}.3^{16}.2^2-2^{29}.3^{20}}=\frac{5.2^{33}.3^{18}-2^{30}.3^{18}.7}{3^{17}.7.2^{31}-2^{29}.3^{20}}\)
\(=\frac{2^{30}.3^{18}.\left(5.2^3-7\right)}{3^{17}.2^{29}.\left(7.2^2-3^3\right)}=2.3.33=198\)
Tính giá trị của mỗi phân số sau:
\(E=\dfrac{11\times3^{29}-\left(3^2\right)^{15}}{2\times3^{14}\times2\times3^{14}}\)
\(G=\dfrac{5\times3^{11}+4\times3^{12}}{3^9\times5^2-3^0\times2^3}\)
\(H=\dfrac{\left(3\times4\times2^{16}\right)^2}{11\times2^{13}\times4^{11}-16^9}\)
\(E=\dfrac{11.3^{29}-3^{2^{15}}}{2.3^{14}.2.3^{14}}\)
\(=\dfrac{11.3-3^{30}}{2^2}=\dfrac{33-3^{30}}{4}\)
\(\dfrac{4^{10}\times9^6+3^{12}\times8^5}{6^{13}\times4-2^{16}\times3^{12}}\)
\(\dfrac{2^4\times2^6}{\left(2^5\right)^2}-\dfrac{2^5\times15^3}{6^3\times10^2}\)
\(\dfrac{\left(-2\right)^{10}\times3^{31}+2^{40}\times\left(-3\right)^6}{\left(-2\right)^{11}\times\left(-3\right)^{31}+2^{41}\times3^6}\)
giải chi tiết giúp mình nhé
tính
a, \(1\times2\times3\times...\times2018-1\times2\times3\times...\times2017^2\)
b,\(1500-\left\{5^2\times2^3-11\times\left[7^2-5\times2^3+8\times\left(11^2-121\right)\right]\right\}\)
Tính S = \(\frac{5\times2^{30}\times6^2\times3^{15}-2^3\times8^9\times3^{17}\times21}{21\times2^{29}\times3^{16}\times4-2^{29}\times\left(3^4\right)^5}\)
AI NHANH MÌNH TICK ( NHỚ GHI RÕ CÁCH GIẢI )
Ta có :
\(S=\frac{5\times2^{30}\times6^2\times3^{15}-2^3\times8^9\times3^{17}\times21}{21\times2^{29}\times3^{16}\times4-2^{29}\times\left(3^4\right)^5}\)
\(S=\frac{5\times2^{30}\times2^2\times3^2\times3^{15}-2^3\times2^{27}\times3^{17}\times3\times7}{3\times7\times2^{29}\times3^{16}\times2^2-2^{29}\times3^{20}}\)
\(S=\frac{5\times2^{32}\times3^{17}-2^{30}\times3^{18}\times7}{7\times2^{31}\times3^{17}-2^{29}\times3^{20}}\)
\(S=\frac{2^{30}\times3^{17}\times\left(5\times2^2-3\times7\right)}{2^{29}\times3^{17}\times\left(2^2\times7-3^3\right)}\)
\(S=\frac{2^{30}\times3^{17}\times\left(-1\right)}{2^{29}\times3^{17}\times1}\)
\(\Rightarrow S=-2\)
Ko viết đề :)
\(S=\frac{5\cdot2^{30}\cdot2^2\cdot3^2\cdot3^{15}-2^3\cdot2^{27}\cdot3^{17}\cdot3\cdot7}{3\cdot7\cdot2^{29}\cdot3^{16}\cdot2^2-2^{29}\cdot3^{20}}\)
\(=\frac{5\cdot2^{32}\cdot3^{17}-2^{30}\cdot3^{18}\cdot7}{3^{17}\cdot7\cdot2^{31}-2^{29}\cdot3^{20}}\)
\(=\frac{2^{30}\cdot3^{17}\left(5\cdot2^2-3\cdot7\right)}{2^{29}\cdot3^{17}\left(7\cdot2^2-3^3\right)}\)
\(=\frac{2\left(20-21\right)}{28-27}\)
\(=\frac{40-42}{1}=-\frac{2}{1}=-2\)
Vậy S= -2
1.Tính giá trị tuyệt đối:(hẹp me)
a)\(\frac{72^3\times54^2}{108^4}\)
b)\(\frac{3^{10}\times11+3^{10}\times5}{3^9\times2^4}\)
c)\(\left(1:\frac{1}{7}\right)^2[\left(2^2\right)^3:2^5]\times\frac{1}{49}\)
d)\(\frac{4^6\times3^5-2^{12}\times3^6}{2^{12}\times9^3+8^4\times3^5}\)
Bài 5 : Tính nhanh :
a, A =\(1993^{1^{2\times3\times4\times.....\times1994}}\)
b, B = \(1994^{\left(225-1^2\right)\times\left(225-2^2\right)\times....\times\left(225-50^2\right)}\)
c, C =\(\frac{2^{10}\times3^{31}+2^{40}\times3^6}{2^{11}\times3^{31}+2^{41}\times3^6}\)
d, D = \(\left(1+2+2^2+2^3+.....+2^{2003}+2^{2004}\right)-2^{2005}\)
Ta có : D = (1 + 2 + 22 + 23 + ....... + 22004) - 22005
Đặt A = 1 + 2 + 22 + 23 + ....... + 22004
=> 2A = 2 + 22 + 23 + ....... + 22005
=> 2A - A = 22005 - 1
=> A = 22005 - 1
Thay vào ta có : D = (1 + 2 + 22 + 23 + ....... + 22004) - 22005
=> D = 22005 - 1 - 22005
=> D = -1
cậu làm còn thiếu bước kìa Nguyễn Việt Hoàng
Tính:
\(\frac{exp\left(24\right)}{\frac{25}{2}\%}\times12\frac{5}{4}+\left|-54^2\right|\times\pi+6\)\(\times7\sqrt{65}+\frac{7\times7^2\times7^3\times7^4}{3\times3^2\times3^3\times3^4}\)