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\(\frac{\left(0,6\right)^{^5}}{\left(0,2\right)^6}=\left(0,6\right)^5:\left(0,2\right)^6=\frac{243}{3125}:\frac{1}{15625}=\frac{243}{3125}.15625=\frac{243.15625}{3125}=\frac{3796875}{3125}=1215\)
\(\frac{\left(0,6\right)^5.\left(0,3\right)^3}{\left(0,2\right)^6.\left(0,3\right)^7}\)
\(=\frac{\left(\frac{6}{10}\right)^5.\left(\frac{3}{10}\right)^3}{\left(\frac{2}{10}\right)^6.\left(\frac{3}{10}\right)^7}\)
\(=\frac{6^5.3^3.\frac{1}{10^8}}{2^6.3^7.\frac{1}{10^{13}}}\)
\(=\frac{2^5.3^5.3^3}{2^6.3^7.\frac{1}{10^5}}\)
\(=\frac{10^5.3}{2}\)
\(=150000\)
c) \(\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{0,625-0,5+\frac{5}{11}+\frac{5}{12}}=\frac{3\left(0,125-0,1+\frac{1}{11}+\frac{1}{12}\right)}{5\left(0,123-0,1+\frac{1}{11}+\frac{1}{12}\right)}=\frac{3}{5}\)
\(\frac{\left(0,6\right)^5}{\left(0,2\right)^6}=\frac{\left(0,2.3\right)^5}{\left(0,2\right)^6}=\frac{\left(0,2\right)^5.3^5}{\left(0,2\right)^6}=\frac{3^5}{0,2}=\frac{243}{0,2}=1215\)
\(a,\frac{2^3.2^4}{2^5}=\frac{2^7}{2^5}=2^2=4\)
\(b,\frac{\left(0,2\right)^5.\left(0,6\right)^4}{\left(0,2\right)^7.\left(0,3\right)^4}=\frac{\left(0,2\right)^5.\left(0,3\right)^4.2^4}{\left(0,2\right)^7.\left(0,3\right)^4}=\frac{2^4}{\left(0,2\right)^2}\)
\(c,\frac{3^3.12^4}{6^5.9^4}=\frac{3^3.6^4.2^4}{6^5.3^8}=\frac{2^4}{6.3^5}=\frac{2^4}{2.3.3^5}=\frac{2^3}{3^6}\)
\(d,\frac{2^3+2^4+2^5}{7^2}=\frac{8+16+32}{49}=\frac{56}{49}=\frac{8}{7}\)
\(e,\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.3^8}{2^6.3^6.2^9}=\frac{2^{15}.3^8}{2^{15}.3^6}=3^2=9\)
\(\frac{\left(0,6\right)^5}{\left(0,2\right)^6}=\frac{\left(0,2\right)^5\cdot3^5}{\left(0,2\right)^6}=\frac{243}{0,2}=1215\)
d) \(\dfrac{8^4.3^6}{2^7.65}=\dfrac{\left(2^3\right)^4.3^6}{2^7.65}=\dfrac{2^{12}.3^6}{2^7.65}=\dfrac{2^7.2^5.3^6}{2^7.65}=\dfrac{2^5.3^6}{65}=\dfrac{23328}{65}\)
c) \(\left(\dfrac{3}{5}-\dfrac{3}{4}\right).\left(\dfrac{2}{6}-\dfrac{1}{5}\right)^2=\dfrac{3.4-3.5}{4.5}.\left(\dfrac{2.5-1.6}{6.5}\right)^2\\ =\dfrac{-3}{20}.\left(\dfrac{2}{15}\right)^2=\dfrac{-3}{20}.\dfrac{4}{225}\\ =\dfrac{-3}{4.5}.\dfrac{4}{75.3}=\dfrac{-1}{375}\)
a) \(\frac{2^5\cdot2^{12}\cdot2^6}{2^{24}}=\frac{2^{23}}{2^{24}}=\frac{1}{2}\)
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\(\frac{\left(0,2.3\right)^5}{0,2^6}\)=\(\frac{0,2^5.3^5}{0,2^6}\)=\(\frac{3^5}{0,2}\)=\(\frac{243}{0,2}\)=1215