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Bài 8:
a: \(\left(\dfrac{2}{5}+\dfrac{3}{4}\right)^2=\left(\dfrac{8+15}{20}\right)^2=\left(\dfrac{23}{20}\right)^2=\dfrac{529}{400}\)
b: \(\left(\dfrac{5}{4}-\dfrac{1}{6}\right)^2=\left(\dfrac{15}{12}-\dfrac{2}{12}\right)^2=\left(\dfrac{13}{12}\right)^2=\dfrac{169}{144}\)
a,\(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2\)
\(=\left(\dfrac{13}{14}\right)^2\)
\(=\dfrac{169}{196}\)
b,\(\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)
\(=\left(\dfrac{-1}{12}\right)^2\)
\(=\dfrac{1}{144}\)
c,\(\dfrac{5^4.20^4}{25^5.4^5}\)
\(=\dfrac{100^4}{100^5}\)
\(=\dfrac{1}{100}\)
d,\(\left(\dfrac{-10}{3}\right)^5.\left(\dfrac{-6}{5}\right)^4\)
\(=\left(\dfrac{-10}{3}\right)^4.\left(\dfrac{-6}{5}\right)^4.\left(\dfrac{-10}{3}\right)\)
\(=\left(\dfrac{\left(-10\right)}{3}.\dfrac{\left(-6\right)}{5}\right)^4.\left(\dfrac{-10}{3}\right)\)
\(=4^4.\left(\dfrac{-10}{3}\right)\)
\(=256.\left(\dfrac{-10}{3}\right)\)
\(=\dfrac{-2560}{3}\)
a) \(\frac{4}{3}-\frac{2}{5}\)
\(=\frac{20}{15}-\frac{6}{15}=\frac{14}{15}\)
b) \(\left|-\frac{1}{10}\right|-\left(-\frac{1}{3}\right)^2\div\frac{5}{9}\)
\(=\frac{1}{10}-\frac{1}{9}\cdot\frac{9}{5}\)
\(=\frac{1}{10}-\frac{1}{5}=\frac{1}{10}-\frac{2}{10}\)
\(=-\frac{1}{10}\)
c) Đề bài có vấn đề!!!
d) \(\left(-0,2\right)^2\cdot5-8^2\cdot\frac{9^4}{3^7}\cdot4^3\)
\(=0,04\cdot5-64\cdot\frac{\left(3^2\right)^4}{3^7}\cdot64\)
\(=0,2-4096\cdot\frac{3^8}{3^7}=0,2-4096\cdot3\)
\(=0,2-12288=-128878\)
a.\(\left(\frac{3}{7}+\frac{1}{2}\right)^2\)
=\(\left(\frac{6}{14}+\frac{7}{14}\right)^2\)
=\(\left(\frac{13}{14}\right)^2\)
=\(\frac{13^2}{14^2}\)
=\(\frac{169}{196}\)
b.\(\left(\frac{3}{4}-\frac{5}{6}\right)^2\)
=\(\left(\frac{9}{12}-\frac{10}{12}\right)^2\)
=\(\left(\frac{-1}{12}\right)^2\)
=\(\frac{-1^2}{12^2}\)
=\(\frac{1}{144}\).
c.Phần C bn viết lại đề bài đi,mk ko hiểu
d.\(\left(\frac{-10}{3}\right)^5.\left(\frac{-6}{5}\right)^4\)
=\(\frac{-10^5}{3^5}.\left(\frac{-6^4}{5^4}\right)\)
=\(\frac{-100000}{243}.\frac{1296}{625}\)
=\(\frac{-2560}{3}\)
Không biết đúng ko nữa
a) \(\frac{7^3.5^8}{49.25^4}=\frac{7^3.5^8}{7^2.\left(5^2\right)^4}=7.\frac{5^8}{5^8}=7\)
b) \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3.3^8.5^2.5^3}{3.5.5^4.3^8}=\frac{5^5}{5^5}=1\)
c) Đề hơi sai roi bạn oi
d) \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2=\left(\frac{-1}{10}\right)^2+\left(\frac{11}{10}\right)^2=\frac{1}{100}+\frac{121}{100}=\frac{61}{50}\)
3.
a) \(\left(x-1\right)^3=125\)
=> \(\left(x-1\right)^3=5^3\)
=> \(x-1=5\)
=> \(x=5+1\)
=> \(x=6\)
Vậy \(x=6.\)
b) \(2^{x+2}-2^x=96\)
=> \(2^x.\left(2^2-1\right)=96\)
=> \(2^x.3=96\)
=> \(2^x=96:3\)
=> \(2^x=32\)
=> \(2^x=2^5\)
=> \(x=5\)
Vậy \(x=5.\)
c) \(\left(2x+1\right)^3=343\)
=> \(\left(2x+1\right)^3=7^3\)
=> \(2x+1=7\)
=> \(2x=7-1\)
=> \(2x=6\)
=> \(x=6:2\)
=> \(x=3\)
Vậy \(x=3.\)
Chúc bạn học tốt!
`a, (4/5 - 1) : 3/5 - 2/3 .0,5`
`= (4/5 - 5/5) . 5/3 - 2/3 . 1/2`
`= (-1)/5 . 5/3 - 1/3`
`= (-1)/3 - 1/3`
`= -2/3`
`b, [10 . 5^(-2) - 25 . (-1/5)^2 + 2] : (-2/5 - (-3)^0)`
`= [10 . 1/25 - 25 . 1/25 + 2] : (-2/5 - 1)`
`= [2/5 -1 + 2] : (-7/5)`
`= 7/5 . (-5/7)`
`= -1`
`c, (4^2 . 25^2 + 32 . 125)/(2^3 . 5^2)`
`= (2^4 . 5^4 + 2^5 . 5^3)/(2^3 . 5^2)`
`= (2^3 . 5^2 . (2 . 5^2 + 2^2 . 5))/(2^3 . 5^2)`
`= 2 . 25 + 4 . 5`
`= 50 + 20`
`= 70`