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Cách viết khác : \(\frac{16}{81}=\frac{2^4}{3^4}=\left(\frac{2}{3}\right)^4\)
Chúc bạn học tốt ^^
\(a,3^{16}:3=3^{16-1}=3^{15}\)
\(b,3^6.3^4.3^2.3=3^{6+4+2+1}=3^{13}\)
\(c,\left(-\frac{1}{4}\right).\left(6\frac{2}{11}\right)+\left(3\frac{9}{11}\right).\left(-\frac{1}{4}\right)=\left(-\frac{1}{4}\right).\frac{68}{11}+\frac{42}{11}.\left(-\frac{1}{4}\right)\)
\(=\left(-\frac{1}{4}\right)\left(\frac{68}{11}+\frac{42}{11}\right)\)
\(=\left(-\frac{1}{4}\right).10\)
\(=-\frac{10}{4}=-\frac{5}{2}\)
\(d,\left(-\frac{1}{2}\right)^3+\frac{1}{2}:5=\left(-\frac{1}{2}\right)\left(\left(\frac{1}{2}\right)^2-\frac{1}{5}\right)\)
\(=-\frac{1}{2}.\left(\frac{1}{4}-\frac{1}{5}\right)\)
\(=-\frac{1}{2}.\frac{1}{20}\)
\(=-\frac{1}{40}\)
\(g,1\frac{1}{25}+\frac{2}{21}-\frac{1}{25}+\frac{19}{21}=\frac{26}{25}+\frac{2}{21}-\frac{1}{25}+\frac{19}{21}\)
\(=\left(\frac{26}{25}-\frac{1}{25}\right)+\left(\frac{2}{21}+\frac{19}{21}\right)\)
\(=1+1\)
\(=2\)
Ta có:
\(\begin{array}{l}{\left( {\frac{1}{4}} \right)^8} = {[{\left( {\frac{1}{2}} \right)^2}]^8} = {(\frac{1}{2})^{2.8}} = {(\frac{1}{2})^{16}};\\{\left( {\frac{1}{8}} \right)^3} = {[{(\frac{1}{2})^3}]^3} = {(\frac{1}{2})^{3.3}} = {(\frac{1}{2})^9}\end{array}\)
