-1/24-[1/4-(1/2-7/8)]
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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.
$(37.8^{1007}-7.2^{3021}):8^{1007}=[37.8^{1007}-7.(2^3)^{1007}]:8^{1007}$
$=[37.8^{1007}-7.8^{1007}]:8^{1007}$
$=8^{1007}(37-7):8^{1007}=37-7=30$
5 tháng 8 2023
P=24(7^2+1)(7^4+1)(7^8+1)(7^16+1)
=> 2P = 48(7^2+1)(7^4+1)(7^8+1)(7^16+1)
= (7^2 - 1)(7^2+1)(7^4+1)(7^8+1)(7^16+1)
= (7^4 - 1)(7^4+1)(7^8+1)(7^16+1)
= (7^8 - 1)(7^8+1)(7^16+1)
= (7^16 - 1)(7^16+1)
= 7^32 - 1
=> P = (7^32 - 1) / 2
D
1
AH
Akai Haruma
Giáo viên
15 tháng 7 2023
Lời giải:
a.
$\frac{5}{15}-\frac{1}{6}\times \frac{2}{5}=\frac{5}{15}-\frac{1}{15}=\frac{4}{15}$
b.
$\frac{8}{24}+\frac{3}{4}:\frac{1}{8}=\frac{1}{3}+6=\frac{19}{3}$
c.
$\frac{1}{7}: \frac{2}{8}-\frac{1}{7}=\frac{1}{7}\times 4-\frac{1}{7}$
$=\frac{1}{7}\times (4-1)=\frac{1}{7}\times 3=\frac{3}{7}$
NT
0
LP
1
21 tháng 2 2023
a) \(\dfrac{2}{5}\cdot\dfrac{1}{7}+\dfrac{2}{5}\cdot\dfrac{5}{7}+\dfrac{2}{5}\)
\(=\dfrac{2}{5}\left(\dfrac{1}{7}+\dfrac{5}{7}+1\right)\)
\(=\dfrac{2}{5}\cdot\dfrac{13}{7}=\dfrac{26}{35}\)
b) \(\dfrac{1}{5}+\dfrac{2}{8}+\dfrac{4}{5}+\dfrac{7}{8}-\dfrac{1}{8}\)
\(=\left(\dfrac{1}{5}+\dfrac{4}{5}\right)+\left(\dfrac{2}{8}+\dfrac{7}{8}-\dfrac{1}{8}\right)\)
\(=1+1=2\)
c)\(\dfrac{24}{36}\cdot\dfrac{10}{12}\cdot36\)
\(=\dfrac{24\cdot10\cdot36}{36\cdot12}=\dfrac{12\cdot2\cdot10\cdot36}{12\cdot36}\)
\(=2\cdot10=20\)
14 tháng 4 2023
a: x=-5/11+2/11=-3/11
b: =>x=-3/24+20/24+1/24=18/24=3/4
c: =>5/8-x=1/9+5/4=4/36+45/36=49/36
=>x=5/8-49/36=-53/72
d: =>2/3-x=1/3
=>x=1/3
e: =>1/5:x=12/35
=>x=7/12
10 tháng 11 2017
\(\text{a) }\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\dfrac{3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\\ =\dfrac{\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\\ \\ =\dfrac{\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\\ =\dfrac{\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)}{3}\\ =\dfrac{\left(2^{16}-1\right)\left(2^{16}+1\right)}{3}\\ =\dfrac{2^{32}-1}{3}\\ \)
\(\text{b) }24\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\\ =\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\\ =\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right) \\ =\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\\ =\left(5^{16}-1\right)\left(5^{16}+1\right)\\ =5^{32}-1\\ \)
\(\text{c) }48\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\left(7^{16}+1\right)\\ =\left(7^2-1\right)\left(7^2+1\right)\left(7^4+1\right)\left(7^8+1\right)\left(7^{16}+1\right)\\ =\left(7^4-1\right)\left(7^4+1\right)\left(7^8+1\right)\left(7^{16}+1\right)\\ =\left(7^8-1\right)\left(7^8+1\right)\left(7^{16}+1\right)\\ =\left(7^{16}-1\right)\left(7^{16}+1\right)\\ =7^{32}-1\)
\(...-\dfrac{1}{24}-\left[\dfrac{1}{4}--\dfrac{3}{8}\right]=-\dfrac{1}{24}-\dfrac{5}{8}=-\dfrac{2}{3}\)
\(-\dfrac{1}{24}-\left[\dfrac{1}{4}-\left(\dfrac{1}{2}-\dfrac{7}{8}\right)\right]\)
\(=-\dfrac{1}{24}-\left[\dfrac{1}{4}-\left(\dfrac{4}{8}-\dfrac{7}{8}\right)\right]\)
\(=-\dfrac{1}{24}-\left(\dfrac{1}{4}+\dfrac{3}{8}\right)\)
\(=-\dfrac{1}{24}-\left(\dfrac{2}{8}+\dfrac{3}{8}\right)\)
\(=-\dfrac{1}{24}-\dfrac{5}{8}\)
\(=-\dfrac{1}{24}-\dfrac{15}{24}\)
\(=\dfrac{-16}{24}\)
\(=-\dfrac{2}{3}\)