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a)\(10^{19}+10^{18}+10^{17}=10^{17}\left(10^2+10+1\right)\)=1017.111=1016.2.5.111=1016.2.555 chia hết cho 555
b)\(81^7-27^9-9^{13}=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)=328-327-326=325(33-32-3)=325.15 chia hết cho 15
c)\(5^7-5^6+5^5=5^5\left(5^2-5+1\right)=5^5.21\) chia hết cho 21
d)\(7^6+7^5-7^4=7^3\left(7^3+7^2-7\right)=7^3.385=7^3.5.77\) chia hết cho 77
\(\sqrt{\frac{9}{25}}+\sqrt{\frac{1}{6}}-\sqrt{\frac{4}{49}}\)\(=\sqrt{\left(\frac{3}{5}\right)^2}+\sqrt{\frac{1}{6}}-\sqrt{\left(\frac{2}{7}\right)^2}\)\(=\frac{3}{5}+\sqrt{\frac{1}{6}}-\frac{2}{7}\)\(=\left(\frac{3}{5}-\frac{2}{7}\right)+\sqrt{\frac{1}{6}}\)\(=\left(\frac{21}{35}-\frac{10}{35}\right)+\sqrt{\frac{1}{6}}\)\(=\frac{11}{35}+\sqrt{\frac{1}{6}}\)\(=\sqrt{\frac{1.6}{6.6}}+\frac{11}{35}\)\(=\frac{\sqrt{6}}{6}+\frac{11}{35}\)\(=\frac{35\sqrt{6}}{210}+\frac{66}{210}\)\(=\frac{35\sqrt{6}+66}{210}\)
(3-1/4+2/3) - (5+1/3-6/5) - (6-7/4+3/2) = 3-1/4+2/3 -5 +1/3 + 6/5 -6 + 7/4 - 3/2
= (3-5-6) + (-1/4 +7/4) + ( 2/3+1/3) + ( 6/5-3/2)
=(-8) + 2+1+ (-3/10)
=5,3
Ta có : \(\frac{x}{\frac{1}{3}}=\frac{y}{\frac{1}{5}}\)
\(\Rightarrow\frac{x\times y}{\frac{1}{3}\times\frac{1}{5}}=\frac{1500}{\frac{1}{15}}=22500\)
\(\Rightarrow\frac{x}{\frac{1}{3}}=22500\Rightarrow x=22500\times\frac{1}{3}=7500\)
\(\Rightarrow\frac{y}{\frac{1}{5}}=22500\Rightarrow y=22500\times\frac{1}{5}=4500\)
(-10/3)^5 . (-6/5)^4
= (-10/3)^4.(-10/3).(-6/5)^4
= [(-10/3).(-6/5)]^4.(-10/3)
= 4^4 . (-10/3)
= 256.(-10/3)
= -2560/3
(3/7)^21:(9/49)^6
=(3/7)^21:[(3/7)^2]^6
=(3/7)^21:(3/7)^12
=(3/7)^21-12
=(3/7)^9