Cho P=12*(5^2+1)(5^4=1)(5^8+1)(5^16+1). Tính P.
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LT
1
T
14 tháng 9 2018
\(12.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(=\frac{24}{2}.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(=\frac{5^2-1}{2}.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(=\frac{5^4-1}{2}.\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(=\frac{5^8-1}{2}.\left(5^8+1\right).\left(5^{16}+1\right)\)
\(=\frac{5^{16}-1}{2}.\left(5^{16}+1\right)\)
\(=\frac{5^{32}-1}{2}\)
KV
21 tháng 10 2023
a) 1 + 1/4 + 1/8 + 1/16
= 16/16 + 4/16 + 2/16 + 1/16
= 23/16
b) 2 - 1/8 - 1/12 - 1/16
= 96/48 - 6/46 - 4/48 - 3/48
= 83/48
c) 4/99 × 18/5 : 12/11 + 3/5
= 8/55 : 12/11 + 3/5
= 2/15 + 3/5
= 2/15 + 9/15
= 11/15
d) (1 - 3/4) × (1 + 1/3) : (1 - 1/3)
= 1/4 × 4/3 : 2/3
= 1/3 : 2/3
= 2
VM
19 tháng 8 2020
Đặt \(A=12.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(\Rightarrow2A=24.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^2-1\right).\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^4-1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^8-1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^{16}-1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^{16}\right)^2-1^2\)
\(2A=5^{32}-1\)
\(\Rightarrow A=\frac{5^{32}-1}{2}.\)
NK
12 tháng 2 2023
\(a,\dfrac{4}{5}+\dfrac{2}{3}+\dfrac{1}{9}=\dfrac{12}{15}+\dfrac{10}{15}+\dfrac{1}{9}=\dfrac{22}{15}+\dfrac{1}{9}=\dfrac{66}{45}+\dfrac{5}{45}=\dfrac{71}{45}\)
\(b,\dfrac{3}{7}+\dfrac{11}{14}+\dfrac{19}{28}=\dfrac{12}{28}+\dfrac{22}{28}+\dfrac{19}{28}=\dfrac{53}{28}\)
\(c,\dfrac{1}{2}+\dfrac{1}{7}+\dfrac{-1}{5}=\dfrac{7}{14}+\dfrac{2}{14}+\dfrac{-1}{5}=\dfrac{9}{14}+\dfrac{-1}{5}=\dfrac{45}{70}+\dfrac{-14}{70}=\dfrac{31}{70}\)
\(d,\dfrac{7}{8}+\dfrac{5}{16}+\dfrac{-3}{4}=\dfrac{14}{16}+\dfrac{5}{16}+\dfrac{-12}{16}=\dfrac{7}{16}\)
\(e,\dfrac{1}{4}+\dfrac{5}{12}+\dfrac{-1}{13}=\dfrac{3}{12}+\dfrac{5}{12}+\dfrac{-1}{13}=\dfrac{8}{12}+\dfrac{-1}{13}=\dfrac{2}{3}+\dfrac{-1}{13}=\dfrac{26}{39}+\dfrac{-3}{39}=\dfrac{23}{39}\)
\(g,\dfrac{2}{3}+\dfrac{3}{8}+\dfrac{-5}{12}=\dfrac{16}{24}+\dfrac{9}{24}+\dfrac{-5}{12}=\dfrac{25}{24}+\dfrac{-5}{12}=\dfrac{25}{24}+\dfrac{-10}{24}=\dfrac{15}{24}\)
LN
1
MA
18 tháng 9 2016
\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^{32}-1\right)\)
\(P=\frac{5^{32}-1}{2}\)
8 tháng 4 2023
1)\(\dfrac{2}{9}+\dfrac{-3}{4}+\dfrac{5}{30}\)
\(=\dfrac{2.20}{9.20}+\dfrac{-3.45}{4.45}+\dfrac{5.6}{30.6}\)
\(=\dfrac{40}{180}+\dfrac{-135}{180}+\dfrac{30}{180}\)
\(=\dfrac{40+\left(-135\right)+30}{180}\)
\(=\dfrac{-65}{180}\)
\(=\dfrac{-13}{36}\)
2)\(\dfrac{-7}{12}-\dfrac{11}{18}\)
\(=\dfrac{-7.3}{12.3}-\dfrac{11.2}{18.2}\)
\(=\dfrac{-21}{36}-\dfrac{22}{36}\)
\(=\dfrac{-21-22}{36}\)
\(=\dfrac{-43}{36}\)
3)\(\dfrac{7}{8}-\dfrac{-5}{16}\)
\(=\dfrac{7.2}{8.2}-\dfrac{-5}{16}\)
\(=\dfrac{14}{16}-\dfrac{-5}{16}\)
\(=\dfrac{14-\left(-5\right)}{16}\)
\(=\dfrac{19}{16}\)
4)\(\dfrac{3}{8}-\dfrac{-9}{10}-\dfrac{5}{16}\)
\(=\dfrac{3.10}{8.10}-\dfrac{-9.8}{10.8}-\dfrac{5.5}{16.5}\)
\(=\dfrac{30}{80}-\dfrac{-72}{80}-\dfrac{25}{80}\)
\(=\dfrac{30-\left(-72\right)-25}{80}\)
\(=\dfrac{77}{80}\)
KT
7 tháng 2 2018
1) \(\frac{1}{12}+\frac{1}{16}+\frac{3}{4}\)
\(=\frac{4}{48}+\frac{3}{48}+\frac{36}{48}\)
\(=\frac{4+3+36}{48}\)
\(=\frac{43}{48}\)
2) a) \(\frac{1}{15}+\frac{4}{15}+\frac{5}{18}+\frac{7}{18}\)
\(=\left(\frac{1}{15}+\frac{4}{15}\right)+\left(\frac{5}{18}+\frac{7}{18}\right)\)
\(=\frac{1}{3}+\frac{2}{3}=1\)
b) \(\frac{1}{8}+\frac{1}{12}+\frac{3}{8}+\frac{5}{12}\)
\(=\left(\frac{1}{8}+\frac{3}{8}\right)+\left(\frac{1}{12}+\frac{5}{12}\right)\)
\(=\frac{1}{2}+\frac{1}{2}=1\)
P= 12.(52+1)(54 +1)(58+1)(516+1)
=>2P=24.(52+1)(54 +1)(58+1)(516+1)
=(52 -1)(52+1)(54+1)(58+1)(516+1)
=(58- 1)(58+1)(516+1)
=(516 -1)(516 -1)
= 532 -1