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Ta có :
\(0,0\left(8\right)=\dfrac{1}{10}.0,\left(8\right)=\dfrac{1}{10}.0,\left(1\right).8=\dfrac{1}{10}.\dfrac{1}{9}.8=\dfrac{4}{45}\)
\(0,1\left(2\right)=0,1+0,0\left(2\right)\)
\(=\dfrac{1}{10}+\dfrac{1}{10}.0,\left(2\right)=\dfrac{1}{10}+\dfrac{1}{10}.0,\left(1\right).2\)
\(=\dfrac{1}{10}+\dfrac{1}{10}.\dfrac{1}{9}.2=\dfrac{9}{90}+\dfrac{2}{90}=\dfrac{11}{90}\)
\(0,1\left(23\right)=0,1+0,0\left(23\right)=\dfrac{1}{10}+\dfrac{1}{10}.0,23\)
\(=\dfrac{1}{10}+\dfrac{1}{10}.0,\left(01\right).23\)
\(\dfrac{1}{10}+\dfrac{1}{10}.\dfrac{1}{99}.23=\dfrac{99}{990}+\dfrac{23}{990}=\dfrac{122}{990}=\dfrac{61}{495}\)
1.
a) x : \(\left(\dfrac{3}{4}\right)^3\) =\(\left(\dfrac{3}{4}\right)^3\)
x = \(\left(\dfrac{3}{4}\right)^3.\left(\dfrac{3}{4}\right)^3\)
x = \(\dfrac{3}{4}^{3+3}\)
x = \(\dfrac{3}{4}^6\)
x = \(\dfrac{729}{4096}\)
b) \(\left(\dfrac{2}{5}\right)^5.x=\left(\dfrac{2}{5}\right)^8\)
x = \(\left(\dfrac{2}{5}\right)^8:\left(\dfrac{2}{5}\right)^5\)
x = \(\dfrac{2}{5}^{8-5}\)
x = \(\dfrac{2}{5}^3\)
x = \(\dfrac{8}{5}\)
2.
(0,36)\(^8\) \([\left(0,6\right)^3]^8\) = (0,6)\(^{3.8}\) = ( 0,6)\(^{24}\)
( 0,216)\(^4\) = \([\left(0,6\right)^3]^4\) = (0.6)\(^{3.4}\) = ( 0,6)\(^{12}\)
\(x:\left(\dfrac{3}{4}\right)^3=\left(\dfrac{3}{4}\right)^2\)
\(x=\left(\dfrac{3}{4}\right)^2.\left(\dfrac{3}{4}\right)^3\) <=> \(x=\left(\dfrac{3}{4}\right)^{2+3}\)
=> \(x=\left(\dfrac{3}{4}\right)^5\)
b, \(\left(\dfrac{2}{5}\right)^5.x=\left(\dfrac{2}{5}\right)^8\)
\(x=\left(\dfrac{2}{5}\right)^8:\left(\dfrac{2}{5}\right)^5\Leftrightarrow x=\left(\dfrac{2}{5}\right)^{8-5}\)
=>\(x=\left(\dfrac{2}{5}\right)^3\)
bài 2 : Với bài này ta cần áp dụng quy tắc: \(\left(x^m\right)^n=x^{m.n}\)
\(0,36^8=\left[\left(0,6\right)^2\right]^8=\left(0,6\right)^{16}\)
\(0,216^4=\left[\left(0,6\right)^3\right]^4=\left(0,6\right)^{12}\)
a: \(=2^2\cdot9\cdot\dfrac{1}{6\cdot9}\cdot\dfrac{4^2}{9^2}=\dfrac{2^2}{6}\cdot\dfrac{2^4}{3^4}=\dfrac{2^6}{2\cdot3\cdot3^4}=\dfrac{2^5}{3^5}=\left(\dfrac{2}{3}\right)^5\)
b: \(=2^8\cdot\dfrac{3^4}{2^4}=3^4\cdot2^4=6^4\)
c: \(=\dfrac{\left(\dfrac{1}{2}\right)^3\cdot2^3\cdot\left(\dfrac{1}{2}\right)^2}{\left(-8\right)^2\cdot16}\cdot2^6=\dfrac{\dfrac{1}{2^2}}{64\cdot16}\cdot64=\dfrac{1}{4}:16=\dfrac{1}{64}=\left(\dfrac{1}{8}\right)^2\)
a: \(=2^2\cdot9\cdot\dfrac{1}{3^3\cdot2}\cdot\dfrac{2^4}{3^4}=\dfrac{2^4\cdot2^2}{2}\cdot\dfrac{9}{3^3\cdot3^4}=\dfrac{2^5}{3^5}=\left(\dfrac{2}{3}\right)^5\)
b: \(=2^8\cdot\dfrac{3^4}{2^4}=3^4\cdot2^4=6^4\)
c: \(=\dfrac{\dfrac{1}{2^3}\cdot\dfrac{1}{2^2}\cdot8}{\left(-8\right)^2\cdot2^4}\cdot2^6=\dfrac{1}{2^2}\cdot2^6:2^{10}=\dfrac{2^4}{2^{10}}=\dfrac{1}{2^6}=\left(\dfrac{1}{8}\right)^2\)
`(1 1/4)^10 . (2/5)^20`
`=(5/4)^10 . (2/5)^20`
`=(5^10 .2^20)/(4^10 .5^20)`
`=(5^10 .4^10)/(4^10 .5^20)`
`=1/(5^10)`
`=(1/5)^10`
a: \(=\dfrac{3^3\cdot2^6}{3^{-4}\cdot2^6}=3^7\)
b: \(=\left(\dfrac{3}{7}\cdot\dfrac{5}{3}\right)^6\cdot\dfrac{5}{3}\cdot\dfrac{3}{7}:\left(\dfrac{7^3}{5^4}\right)^{-2}\)
\(=\left(\dfrac{5}{7}\right)^6\cdot\dfrac{5}{7}\cdot\left(\dfrac{5}{7}\right)^6\cdot5^2\)
\(=\left(\dfrac{5}{7}\right)^{13}\cdot5^2\)
c: \(=5^4\cdot2.5^{-5}\cdot125\cdot0.04\)
\(=5^4\cdot5\cdot\left(\dfrac{5}{2}\right)^{-5}\)
\(=5^5\cdot\left(\dfrac{2}{5}\right)^5=2^5\)
a: \(=\dfrac{3^3\cdot2^6}{3^{-4}\cdot2^6}=3^7\)
b: \(=\left(\dfrac{3}{7}\right)^5\cdot\left(\dfrac{3}{7}\right)\cdot\dfrac{5^6}{3^6}:\left(\dfrac{625}{343}\right)^2\)
\(=\dfrac{3^6}{7^6}\cdot\dfrac{5^6}{3^6}:\dfrac{5^8}{7^6}\)
\(=\dfrac{1}{5^2}\)
c: \(=5^{4+3}\cdot\left(\dfrac{5}{2}\right)^{-5}\cdot\dfrac{1}{25}\)
\(=5^5\cdot\left(\dfrac{2}{5}\right)^5=2^5\)
làm bài 3 BĐT
theo bảng xét dấu
còn bài 1,2 ở trên là 1.1 và 1.2 đều trg bài 1.2
bài 1.2 (tức bài 2 ở trên )làm a,b,c,d
\còn bài 2( tức bài 2 ở trên) làm hết
Các câu đúng: b,e
Các câu sai: a, c, d; f.
a) \(\left(-5\right)^2.\left(-5\right)^3=\left(-5\right)^5\);
c) \(\left(0,2\right)^{10}:\left(0,2\right)^5=\left(0,2\right)^{10-5}=0,2^5\);
d) \(\left[\left(-\dfrac{1}{7}\right)^2\right]^4=\left(-\dfrac{1}{7}\right)^{2.4}=\left(-\dfrac{1}{7}\right)^8\)
f \(\dfrac{8^{10}}{4^8}=\dfrac{\left(2^3\right)^5}{\left(2^2\right)^8}=\dfrac{2^{15}}{2^{16}}=\dfrac{1}{2}\)
\(\left(0,09\right)^3=\left(\dfrac{9}{100}\right)^3=\left[\left(\dfrac{3}{10}\right)^2\right]^3=\left(\dfrac{3}{10}\right)^6\\ \left(\dfrac{3}{10}\right)^8=\left(\dfrac{3}{10}\right)^8\\ \left(0,027\right)^2=\left(\dfrac{27}{1000}\right)^2=\left[\left(\dfrac{3}{10}\right)^3\right]^2=\left(\dfrac{3}{10}\right)^6\)