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a, (\(\dfrac{9}{4}\))5 : (\(\dfrac{1}{4}\))5
= (\(\dfrac{9}{4}\) : \(\dfrac{1}{4}\))5
= 95
= 59049
b, 182 : 92
= (18:9)2
= 22
= 4
c, [(-2)\(^4\)]3
= 212
= 4096
d, 57.(\(\dfrac{1}{5}\))7
= (5.\(\dfrac{1}{5}\))7
= 17
= 1
e, (6,5)3: (6,5)2
= 6,5
\(a,\left(\frac{3}{8}+-\frac{3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
= \(\left(-\frac{3}{8}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
= \(\frac{5}{24}:\frac{5}{6}+\frac{1}{2}\)
= \(\frac{1}{4}+\frac{1}{2}\)
= \(\frac{3}{4}\)
b)\(-\frac{7}{3}.\frac{5}{9}+\frac{4}{9}.\left(-\frac{3}{7}\right)+\frac{17}{7}\)
=\(-\frac{35}{27}+\left(-\frac{4}{21}\right)+\frac{17}{7}\)
= \(-\frac{35}{27}+\frac{47}{21}\)
= \(\frac{178}{189}\)
c) \(\frac{117}{13}-\left(\frac{2}{5}+\frac{57}{13}\right)\)
= \(\frac{117}{13}-\frac{311}{65}\)
= \(\frac{274}{65}\)
d) \(\frac{2}{3}-0,25:\frac{3}{4}+\frac{5}{8}.4\)
= \(\frac{2}{3}-\frac{1}{4}:\frac{3}{4}+\frac{5}{8}.4\)
= \(\frac{2}{3}-\frac{1}{3}+\frac{5}{2}\)
= \(\frac{1}{3}+\frac{5}{2}\)
= \(\frac{17}{6}\)
7^6+7^5+7^4 chia hết cho 11
= 7^4.2^2+7^4.7+7^4
= 7^4.(2^2+7+1)
= 7^4. 11
Vì tích này có số 11 nên => chia hết cho 7
a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
a) 1/4(x-3)+2=1/5
1/4.(x-3) = 1/5-2
1/4.(x-3) = -9/5
x-3 = (-9/5):1/4
x-3 = -36/5
x = -36/5+3
x= -21/5
1.
a) \(\left(\frac{1}{5}\right)^3.10^3\)
\(=\left(\frac{1}{5}.10\right)^3\)
\(=2^3\)
\(=8.\)
b) \(\left(-\frac{2}{5}\right)^4:2^4\)
\(=\left[\left(-\frac{2}{5}\right):2\right]^4\)
\(=\left(-\frac{1}{5}\right)^4\)
\(=\frac{1}{625}.\)
c) \(32^2:4^3\)
\(=\left(2^5\right)^2:\left(2^2\right)^3\)
\(=2^{10}:2^6\)
\(=2^4\)
\(=16.\)
d) \(\left(\frac{2}{3}\right)^4:9^2\)
\(=\left(\frac{2}{3}\right)^4:\left(3^2\right)^2\)
\(=\left(\frac{2}{3}\right)^4:3^4\)
\(=\left(\frac{2}{3}:3\right)^4\)
\(=\left(\frac{2}{9}\right)^4\)
\(=\frac{16}{6561}.\)
Chúc bạn học tốt!