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LM
Lê Minh Vũ
VIP
14 tháng 6 2023
\(\left(-\dfrac{1}{2}\right)^2\div\dfrac{1}{4}-2\times\left(-\dfrac{1}{2}\right)^2\\= \dfrac{1}{4}\div\dfrac{1}{4}-2\times\dfrac{1}{4}\\ =1-\dfrac{1}{2}\\ =\dfrac{1}{2}\)
\(\left(-2\right)^3\times-\dfrac{1}{24}+\left(\dfrac{4}{3}-1\dfrac{5}{6}\right)\div\dfrac{5}{12}\)
= \(-6\times-\dfrac{1}{24}+\left(\dfrac{4}{3}-\dfrac{11}{6}\right)\div\dfrac{5}{12}\)
= \(\dfrac{1}{4}+-\dfrac{1}{2}\div\dfrac{5}{12}\)
= \(\dfrac{1}{4}+-\dfrac{6}{5}\)
= \(\dfrac{1}{4}-\dfrac{6}{5}\)
= \(-\dfrac{19}{20}\)
\(\left(6\dfrac{4}{9}+\dfrac{7}{11}\right)-\left(4\dfrac{4}{9}-2\dfrac{4}{11}\right)\\ =\dfrac{58}{9}+\dfrac{7}{11}-\dfrac{40}{9}+\dfrac{26}{11}\\ =\dfrac{58}{9}-\dfrac{40}{9}+\dfrac{7}{11}+\dfrac{26}{11}\\ =12+3\\ =15\)
TA
14 tháng 6 2023
\(a,\left(\dfrac{-1}{2}\right)^2:\dfrac{1}{4}-2\left(-\dfrac{1}{2}\right)^2\)
\(=\left(-\dfrac{1}{2}\right)^2\left(4-2\right)\)
\(=\dfrac{1}{4}.2=\dfrac{1}{2}\)
\(b,\left(-2\right)^3.\dfrac{-1}{24}+\left(\dfrac{4}{3}-1\dfrac{5}{6}\right):\dfrac{5}{12}\)
\(=\left(-8\right).\dfrac{-1}{24}+\left(-\dfrac{1}{2}\right).\dfrac{12}{5}\)
\(=\dfrac{1}{3}+\left(-\dfrac{1}{5}\right)=\dfrac{2}{15}\)
\(c,\left(6\dfrac{4}{9}+\dfrac{7}{11}\right)-\left(4\dfrac{4}{9}-2\dfrac{4}{11}\right)\)
\(=\dfrac{701}{99}-\dfrac{206}{99}=\dfrac{495}{99}=5\)
\(d,10\dfrac{1}{5}-5\dfrac{1}{2}.\dfrac{60}{11}+\dfrac{3}{15\%}\)
\(=\dfrac{51}{5}-30+20=\dfrac{1}{5}\)
\(e,\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{2}{11}-\dfrac{5}{7}.\dfrac{14}{11}\)
\(=\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}.\left(-\dfrac{7}{11}\right)\)
\(=-\dfrac{5}{11}\)
\(f,\dfrac{-5}{7}.\dfrac{2}{11}+\left(-\dfrac{5}{7}\right).\dfrac{9}{11}+1\dfrac{5}{7}\)
\(=\left(-\dfrac{5}{7}\right)\left(\dfrac{2}{11}+\dfrac{9}{11}\right)+\dfrac{12}{7}\)
\(=\left(-\dfrac{5}{7}\right)+\dfrac{12}{7}=1\)
BK
28 tháng 11 2017
\(7\cdot2^{3x+1}-12=2^2\cdot5^2\)
\(\Rightarrow7\cdot2^{3x+1}-12=100\)
\(\Rightarrow7\cdot2^{3x+1}=100+12=112\)
\(\Rightarrow2^{3x+1}=\dfrac{112}{7}=16=2^4\)
\(\Rightarrow3x+1=4\Rightarrow3x=3\Rightarrow x=1\)
Vậy x = 1
AH
Akai Haruma
Giáo viên
21 tháng 10 2023
1.
$(5^{1986}-5^{1985}):5^{1985}=5^{1985}(5-1):5^{1985}=5-1=4$
2.
\((7^{846}+7^{847}):7^{846}=7^{846}(1+7):7^{846}=1+7=8\)
3.
\((9^{2018}-3^{4036}):6^{2006}=[(3^2)^{2018}-3^{4036}]:6^{2006}\)
$=(3^{4036}-3^{4036}):6^{2006}=0:6^{2006}=0$
4.
$(7^{80}.8^{70}-56^{70}):56^{70}$
$=[7^{10}(7.8)^{70}-56^{70}]:56^{70}$
$=[7^{10}.56^{70}-56^{70}]:56^{70}$
$=56^{70}(7^{10}-1):56^{70}=7^{10}-1$
AH
Akai Haruma
Giáo viên
21 tháng 10 2023
5.
$4^{4016}:(4^{4017}-4^{4016})=4^{4016}:[4^{4016}(4-1)]$
$=4^{4016}:4^{4016}:3=1:3=\frac{1}{3}$
6.
$(12^{206}.2^{207}-24^{206}):24^{206}$
$=(12^{206}.2^{206}.2-24^{206}):24^{206}$
$=[(12.2)^{206}.2-24^{206}]:24^{206}$
$=(24^{206}.2-24^{206}):24^{206}$
$=24^{206}(2-1):24^{206}=2-1=1$
7.
$(5^2-24)^{8946}+4^{30}:2^{60}=1^{8946}+(2^2)^{30}:2^{60}$
$=1+2^{60}:2^{60}=1+1=2$
8.
$(37.8^{1007}-7.2^{3021}):8^{1007}=[37.8^{1007}-7.(2^3)^{1007}]:8^{1007}$
$=[37.8^{1007}-7.8^{1007}]:8^{1007}$
$=8^{1007}(37-7):8^{1007}=37-7=30$
GN
GV Nguyễn Trần Thành Đạt
Giáo viên
3 tháng 8 2023
\(2\left(x-3\right)+2^3=3^2.2\\ 2\left(x-3\right)=18-8\\ 2\left(x-3\right)=10\\ x-3=\dfrac{10}{2}\\ x-3=5\\ x=5+3\\ x=8\\ ----\\ 2^2.3-3\left(x-4\right)=2^3-2\\ 12-3\left(x-4\right)=6\\ 3\left(x-4\right)=12-6\\ 3\left(x-4\right)=6\\ x-4=6:3\\ x-4=2\\ x=2+4\\ x=6\\ ----\\ 7.2^2-4\left(2x+1\right)=2^3\\ 28-4\left(2x+1\right)=8\\ 4\left(2x+1\right)=28-8\\ 4\left(2x+1\right)=20\\ 2x+1=20:4\\ 2x+1=5\\ 2x=5-1\\ 2x=4\\ x=\dfrac{4}{2}=2\\ ---\\ 600-2\left(x-3\right)^8=11.2^3\\ 600-2\left(x-3\right)^8=88\\ 2\left(x-3\right)^8=600-88\\ 2\left(x-3\right)^8=512\\ \left(x-3\right)^8=\dfrac{512}{2}\\ \left(x-3\right)^8=256=2^8=\left(-2\right)^8\\ x-3=2.hoặc.x-3=-2\\ x=5.hoặc.x=1\)
KV
20 tháng 12 2023
a) (x - 5).(-10) = -70
x - 5 = -70 : (-10)
x - 5 = 7
x = 7 + 5
x = 12
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
20 tháng 12 2023
b, (+3).(+9).10
= 27.10
= 270
c,(-5).7.2
= (-5.2).7
= -10.7
= -70
d, (-12).13.(-5)
= [-12.(-5)].13
= 60.13
= 780
e, (-150).(-4)
= 150.4
= 600
\(x^2-7.2^2=12+\left(-4\right)\\< =>x^2-28=8\\ < =>x^2=36\\ < =>x=+-6\)
x^2 - 7.2^2 =12+(-4)
x^2 - 7.4 = 8
x^2 - 7 = 8:4
x^2 - 7 = 2
x^2= 9
x^2 = 3^2
Vậy x = 3