So sánh :
\(\left(0,6\right)^9và\left(-0,9\right)^6\)
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329 = (25)9 = 245 < 252 = (24)13=1613<1813
=> (-32)9 > (-18)13
Ta thấy:
25^5=(5^2)^5=5^(2*5)=5^10>5^9.
=>1/5^9>1/25^5.
=>-1/5^9<-1/25^5.
=>(-1/5)^9<(-1/25)^5.
Vậy ...
\(\left(\frac{1}{243}\right)^9=\left(\frac{1}{3^4}\right)^9=\frac{1}{3^{4.9}}=\frac{1}{3^{36}}\)
\(\left(\frac{1}{83}\right)^{13}\frac{1}{3^{42}}\Rightarrow\left(\frac{1}{81}\right)^{13}
a: \(=\left\{\left[\left(20-\dfrac{1}{4}\right)\cdot0.2\right]+\dfrac{3}{20}\right\}\cdot5:\left[\left(2+\dfrac{25}{11}\cdot\dfrac{22}{100}\cdot10\right)\cdot\dfrac{1}{33}\right]\)
\(=\left\{\left[\dfrac{79}{20}+\dfrac{3}{20}\right]\right\}\cdot5:\left[\dfrac{356}{55}\cdot\dfrac{1}{33}\right]\)
\(=\dfrac{82}{20}\cdot5:\dfrac{3856}{1815}\simeq104,516\)
b: \(=\dfrac{13}{30}+\dfrac{28}{45}\cdot\dfrac{5}{2}\cdot\left[\dfrac{5}{6}:\dfrac{53}{90}\right]\cdot\dfrac{53}{50}\)
\(=\dfrac{13}{30}+\dfrac{14}{9}\cdot\dfrac{3}{2}=\dfrac{83}{30}\)
c) \(\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{0,625-0,5+\frac{5}{11}+\frac{5}{12}}=\frac{3\left(0,125-0,1+\frac{1}{11}+\frac{1}{12}\right)}{5\left(0,123-0,1+\frac{1}{11}+\frac{1}{12}\right)}=\frac{3}{5}\)