Rút gọn pân số:\(\frac{20^{20}.3^{40}.6^{20}}{12^{50}.3^{15}}\)
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BA
24 tháng 11 2019
\(a,A=\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
\(=\sqrt{\left(\sqrt{5}^2+2\sqrt{5}+2\sqrt{2}\cdot\sqrt{5}\right)+\sqrt{2}^2+2\sqrt{2}\cdot1+1^2}\)
\(=\sqrt{\sqrt{5}^2+2\cdot\sqrt{5}\left(\sqrt{2}+1\right)+\left(\sqrt{2}+1\right)^2}\)
\(=\sqrt{\left(\sqrt{5}+\sqrt{2}+1\right)^2}\)
\(=\sqrt{5}+\sqrt{2}+1\)
\(b,B=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
\(=\left(\frac{3\cdot\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}{\sqrt{6}+1}+\frac{2\left(\sqrt{6}-2\right)\left(\sqrt{6}+2\right)}{\sqrt{6}-2}-\frac{4\left(3-\sqrt{6}\right)\left(3+\sqrt{6}\right)}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
\(=\left[3\cdot\left(\sqrt{6}-1\right)+2\left(\sqrt{6}+2\right)-4\left(3+\sqrt{6}\right)\right]\left(\sqrt{6}+11\right)\)
\(=\left(\sqrt{6}+11\right)\left(\sqrt{6}-11\right)=-115\)
TT
1
21 tháng 9 2017
\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{20}\cdot2^{20}-2^{20}+2^{20}\cdot3^{20}}{2^{20}\cdot3^{20}-3^{20}+3^{20}\cdot3^{20}}=\frac{2^{20}\left[2^{20}-1+3^{20}\right]}{3^{20}\left[2^{20}-1+3^{20}\right]}=\frac{2^{20}}{3^{20}}\)
ND
2
H9
HT.Phong (9A5)
CTVHS
5 tháng 3 2023
A) \(\dfrac{5}{10}-\dfrac{2}{15}\)
\(=\dfrac{1}{2}-\dfrac{2}{15}\)
\(=\dfrac{15}{30}-\dfrac{4}{30}\)
\(=\dfrac{11}{30}\)
B)\(\dfrac{5}{20}-\dfrac{1}{6}\)
\(=\dfrac{1}{4}-\dfrac{1}{6}\)
\(=\dfrac{6}{24}-\dfrac{4}{24}\)
\(=\dfrac{2}{24}=\dfrac{1}{12}\)
C) \(\dfrac{6}{18}-\dfrac{6}{24}\)
\(=\dfrac{1}{3}-\dfrac{1}{4}\)
\(=\dfrac{4}{12}-\dfrac{3}{12}\)
\(=\dfrac{1}{12}\)
D) \(\dfrac{5}{9}-\dfrac{3}{12}\)
\(=\dfrac{5}{9}-\dfrac{1}{4}\)
\(=\dfrac{20}{36}-\dfrac{9}{36}\)
\(=\dfrac{11}{36}\).
5 tháng 3 2023
a: =1/2-2/15
=15/30-4/30
=11/30
b: =1/4-1/6
=3/12-2/12
=1/12
c: =1/3-1/4
=1/12
d: =20/36-9/36
=11/36
NT
2
30 tháng 6 2015
\(A=\frac{4^{15}.5^{15}.3^{12}.5^{12}}{5^{28}.2^{14}.3^{14}.2^{15}}=\frac{2.2^{29}.5^{27}.3^{12}}{5.5^{27}.2^{29}.3^{12}.3^2}=\frac{2}{45}\)
MT
30 tháng 6 2015
\(A=\frac{20^{15}.15^{12}}{25^{14}.6^{14}.8^5}=\frac{\left(2^2.5\right)^{15}.\left(3.5\right)^{12}}{\left(5^2\right)^{14}.\left(2.3\right)^{14}.\left(2^3\right)^5}=\frac{\left(2^2\right)^{15}.5^{15}.3^{12}.5^{12}}{5^{28}.2^{14}.3^{14}.2^{15}}\)
=\(\frac{2^{30}.3^{12}.5^{15}.5^{12}}{5^{28}.3^{14}.2^{14}.2^{15}}=\frac{2^{30}.3^{12}.5^{27}}{5^{28}.3^{14}.2^{29}}=\frac{2}{5.3^2}=\frac{2}{45}\)
25 tháng 7 2018
12/18 + 12/42 = 2/3 + 2/7 = 14/21 + 6/21 = 20/21
1/2 + 2/4 + 3/6 + 4/8 + 5/10 + 6/12
= 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2
= 1/2 x 6
=6/2
=3
PB
3
19 tháng 6 2023
a. 18/72 = 1/4
15/20 = 3/4
vì 1/4<3/4 nên 18/72<15/20
b. 24/36 = 2/3
20/50 = 2/5
2/3>2/5 nên 24/36>20/50
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
19 tháng 6 2023
a, \(\dfrac{18}{72}\) = \(\dfrac{18:18}{72:18}\) = \(\dfrac{1}{4}\); \(\dfrac{15}{20}\) = \(\dfrac{3}{4}\)
Vì \(\dfrac{1}{4}\) < \(\dfrac{3}{4}\) nên \(\dfrac{18}{72}\) < \(\dfrac{15}{20}\)
b, \(\dfrac{24}{36}\) = \(\dfrac{24:12}{36:12}\) = \(\dfrac{2}{3}\); \(\dfrac{20}{50}\) = \(\dfrac{20:10}{50:10}\) = \(\dfrac{2}{5}\)
Vì \(\dfrac{2}{3}\) > \(\dfrac{2}{5}\) nên \(\dfrac{24}{36}\) > \(\dfrac{20}{50}\)
\(\frac{20^{20}.3^{40}.6^{20}}{12^{50}.3^{15}}\)=\(\frac{2^{20}.3^{40}.2^{20}.3^{20}}{3^{50}.2^{100}.3^{15}}\)=\(\frac{2^{40}.3^{60}:\left(2^{40}.3^{60}\right)}{2^{100}.3^{65}:\left(2^{40}.3^{60}\right)}\)=\(\frac{1}{2^{60}.35}\)