bấm máy tính ra kết quả là 983/504

1/ Bg

\(\frac{21^4}{27.\left(-343\right)}\)= \(\frac{\left(3.7\right)^4}{3^3.\left(-7\right)^3}\)

= \(\frac{3^4.7^4}{3^3.\left(-7\right)^3}\)

= \(\frac{3.\left(-7\right)}{1.1}\)

= 3.(-7)

= -21

2/ Bg

Ta có: \(\frac{a}{4}=\frac{b}{5}=\frac{c}{2}\)và a + b - c = 21                      (a, b, c thuộc Z)

Áp dụng tính chất dãy tỉ số bằng nhau, ta có:

\(\frac{a}{4}=\frac{b}{5}=\frac{c}{2}=\frac{a+b-c}{4+5-2}=\frac{21}{7}\)= 3

=> a = 3.4 = 12

=> b = 3.5 = 15

=> c = 3.2 = 6

Vậy a = 12, b = 15 và c = 6

\(=\frac{\left(3.7\right)^4}{3^3.\left(-7\right)^3}+7\)

\(=\frac{3^4.7^4}{3^3.\left(-7\right)^3}+7\)

=\(\) 3.(-7)+7

= -14

\(\frac{21^4}{27.\left(-343\right)}+7\)

=> \(\frac{\left(3.7\right)^4}{3^3.\left(-7\right)^3}+7=>\frac{3^3.3.7^3.7}{3^3.\left(-7\right)^3}+7\)

=> 3 . (-7) + 7

= -21 + 7 = -14

\(\frac{21^4}{27.\left(-343\right)}+7\)

= \(\frac{\left(3.7\right)^4}{3^3.\left(-7\right)^3}+7\)

= \(\frac{3^4.7^4}{3^3.\left(-7\right)^3}+7\)

= 3.(-7) + 7

= (-21) + 7

= -14.

Chúc bạn học tốt!

\(\left(5-\frac{2}{3}+\frac{3}{7}\right):\left(24-25+\frac{4}{21}-\frac{8}{21}\right)\)

\(\left(\frac{5.21-14+9}{21}\right):\left(\frac{-21-4}{21}\right)\)=\(\left(\frac{5.21-5}{21}\right).\left(\frac{21}{-25}\right)\)=\(\frac{5\left(21-1\right)}{\left(-5\right).5}=\frac{20}{-5}\)

=-4

-0.9615384315

\(=\frac{12}{7}\cdot\frac{3}{4}-\frac{6}{7}\cdot\frac{4}{3}+\frac{6}{7}\)

\(=\frac{6}{7}\left(\frac{3}{2}-\frac{4}{3}+1\right)\)

\(=\frac{6}{7}\left(\frac{1}{6}+1\right)=\frac{6}{7}\cdot\frac{7}{6}=1\)

2.

\(=2017\cdot2018\cdot\left[\left(2016\cdot2018\right)-\left(2016\cdot2017\right)\right]\)

\(=2017\cdot2018\cdot2016\left(2018-2017\right)=2016\cdot2017\cdot2018\)

3.

\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)....\left(\frac{1}{100}-1\right)=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot....\cdot\frac{99}{100}\)

\(=\frac{1}{100}\)

4.

\(=\frac{1+2+2^2+2^4+...+2^9}{2\left(1+2+2^2+2^3+2^4+...+2^9\right)}\)

\(=\frac{1}{2}\)

mình chỉ làm được câu 3 thôi

có \(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)....\left(\frac{1}{100}-1\right)\)

\(=\frac{-1}{2}\times\frac{-2}{3}\times....\times\frac{-99}{100}\)

\(=\frac{\left(-1\right)\left(-2\right)....\left(-99\right)}{2\times3\times....\times100}\)

\(=\frac{-\left(1\times2\times....\times99\right)}{2\times3\times....\times100}\)

\(=\frac{-1}{100}\)

Câu 3 như kiên nhé!! nhầm tí !! xl!

a)     \(1\frac{3}{19}+\frac{8}{21}-\frac{3}{19}+0.5+\frac{13}{21}\)

\(=\left(1\frac{3}{19}-\frac{3}{19}\right)+\left(\frac{8}{21}+\frac{13}{21}\right)+0.5\)

\(=1+1+0.5=2.5\)

b)  \(\left(-\frac{3}{4}+\frac{2}{7}\right):\frac{3}{7}+\left(\frac{5}{7}+\frac{-1}{4}\right):\frac{3}{7}\)

\(=\left(\frac{-3}{4}+\frac{2}{7}+\frac{5}{7}+\frac{-1}{4}\right):\frac{3}{7}\)

\(=0:\frac{3}{7}=0\)

a) \(9^8=\left(3^2\right)^8=3^{16}\)

\(27^3=\left(3^3\right)^3=3^9\)

\(81^2=\left(3^4\right)^2=3^8\)

\(\Leftrightarrow3^{16}:\left(3^9.3^8\right)\)

\(\Leftrightarrow3^{16}:3^{17}\)

\(\Leftrightarrow3^{-1}=\frac{1}{3}\)

a) 9^́́́8 : ̣(27³ . 81²)= 3^{16  :} 3⁹ . 3⁸ = 3¹⁵

b) \(125^4=\left(5^3\right)^4=5^{12}\)

\(343^3=\left(7^3\right)^3=7^9\)

\(=\frac{5^{12}.7^{10}}{5^{12}.7^9}\)

\(=\frac{7^{10}}{7^9}\)

\(=7\)

a) Ta có: \(\dfrac{5}{8}+\dfrac{3}{17}+\dfrac{4}{18}+\dfrac{20}{-17}+\dfrac{-2}{9}+\dfrac{21}{56}\)

\(=\left(\dfrac{3}{17}-\dfrac{20}{17}\right)+\left(\dfrac{2}{9}-\dfrac{2}{9}\right)+\left(\dfrac{5}{8}+\dfrac{3}{8}\right)\)

\(=-1+1=0\)

b) Ta có: \(\left(\dfrac{9}{16}+\dfrac{8}{-27}\right)+\left(1+\dfrac{7}{16}+\dfrac{-19}{27}\right)\)

\(=\left(\dfrac{9}{16}+\dfrac{7}{16}\right)+\left(\dfrac{-8}{27}-\dfrac{19}{27}\right)+1\)

=1-1+1=1