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2a) \(\frac{3^6+45^4-15^3.4^5}{27^4.25^3+45^6}\)
= \(\frac{3^6+\left(3^2.5\right)^4-\left(3.5\right)^3.\left(2^2\right)^5}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}\)
= \(\frac{3^6+3^8.5^4-3^3.5^3.4^{10}}{3^{12}.5^6-3^{12}.5^6}=\frac{3^3.\left(3^3+3^5.5^4-5^3.4^{10}\right)}{0}\)(xem lại đề)
b) \(\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{16}{3}\right)^3:\left(\frac{4}{9}\right)^3}{2^7.5^2+512}\)
= \(\frac{\left(\frac{2}{5}.5\right)^7+\left(\frac{16}{3}:\frac{4}{9}\right)^3}{2^7.5^2+2^9}\)
= \(\frac{2^7+12^3}{2^7\left(5^2+2^2\right)}\)
= \(\frac{2^7+\left(2^2.3\right)^3}{2^7.29}\)
= \(\frac{2^7+2^6.3^3}{2^7.29}\)
= \(\frac{2^6\left(1+27\right)}{2^7.29}=\frac{28}{2.29}=\frac{14}{29}\)
15: Tính
a) Ta có: \(\frac{3^6\cdot45^4-15^{13}\cdot5^{-9}}{27^4\cdot25^3+45^6}\)
\(=\frac{3^6\cdot3^4\cdot15^4-15^{13}\cdot\frac{1}{5^9}}{9^4\cdot3^4\cdot5^6+9^6\cdot5^6}\)
\(=\frac{3^6\cdot45^4-\frac{5^{13}\cdot3^{13}}{5^9}}{9^4\cdot5^6\left(3^4+9^2\right)}\)
\(=\frac{45^4\cdot3^6-5^4\cdot3^{13}}{45^4\cdot5^2\cdot2\cdot9^2}\)
\(=\frac{5^4\cdot3^6\left(9^4-3^7\right)}{5^2\cdot3^4\cdot45^4\cdot2}\)
\(=\frac{5^2\cdot3^2\cdot\left(3^8-3^7\right)}{45^4\cdot2}\)
\(=\frac{5^2\cdot3^9\cdot\left(3-1\right)}{5^4\cdot3^8\cdot2}\)
\(=\frac{1}{5^2}\cdot3\)
\(=\frac{3}{25}\)
a) \(7^6+7^5-7^4=\left(7^4.7^2\right)+\left(7^3.7^2\right)-\left(7^2.7^2\right)=7^2\left(7^4+7^3+7^2\right)=7^2.1793\)
Mà 1793 chia hết cho 11 => 72.1793 chia hết cho 11
a) \(\sqrt{25}-\sqrt{\dfrac{49}{4}}+\sqrt{0,25}\)
\(=5-3,5+0,5\)
\(=2\)
b) \(\left(-\dfrac{25}{24}-\dfrac{31}{42}\right)-\left(\dfrac{-7}{27}-\dfrac{3}{42}\right)\)
\(=\dfrac{-25}{24}-\dfrac{31}{42}+\dfrac{7}{27}+\dfrac{3}{42}\)
\(=\left(\dfrac{-25}{24}+\dfrac{7}{27}\right)+\left(-\dfrac{31}{42}+\dfrac{3}{42}\right)\)
\(=-\dfrac{169}{216}+-\dfrac{2}{3}=-1\dfrac{97}{216}\)
c) \(\dfrac{103}{10}-\left(9,5-0,25.18\right):0,5\)
\(=10,3-\left(9,5-0,25.18\right):0,5\)
\(=10,3-5:0,5\)
\(=0,3\)
d) \(\left(10^3+15.10^2+5^3\right):7\)
\(=\left(10^3+10^2\right)\left(15+5^3\right):7\)
\(=\left(1100.140\right):7\)
\(=22000\)
\(\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)=\(\frac{3^6.3^8.5^4-5^{13}.3^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)=\(\frac{3^{14}.5^4-5^4.3^{13}}{3^{12}.5^6+3^{12}.5^6}\)=\(\frac{3.1.}{1.5^2.}\)=\(\frac{3}{25}\)
Học tốt