a: \(4\frac{5}{16}+\frac{4}{23}-\frac{5}{16}+\frac{19}{23}\)
\(=4+\frac{5}{16}-\frac{5}{16}+\left(\frac{4}{23}+\frac{19}{23}\right)\)
=4+1
=5
b: \(\left(0,125\right)\cdot\left(-4,7\right)\cdot\left(-2\right)^3\)
\(=\frac18\cdot4,7\cdot8\)
=4,7
c: \(12\frac14\cdot\frac34-4\frac14\cdot\frac34\)
\(=\frac34\left(12+\frac14-4-\frac14\right)\)
\(=\frac34\cdot8=6\)
d: \(\frac{15}{14}:\frac57-\frac{29}{14}:\frac57\)
\(=\left(\frac{15}{14}-\frac{29}{14}\right):\frac57=-1\cdot\frac75=-\frac75\)
e: \(\frac{15}{19}\cdot\frac23-\frac{7}{19}\cdot\frac23+\frac83\cdot\frac{17}{19}\)
\(=\frac23\left(\frac{15}{19}-\frac{7}{19}\right)+\frac{8}{19}\cdot\frac{17}{3}\)
\(=\frac23\cdot\frac{8}{19}+\frac{8}{19}\cdot\frac{17}{3}=\frac{8}{19}\cdot\frac{19}{3}=\frac83\)
f: \(\frac18\cdot\sqrt{64}-10\cdot\sqrt{\frac{4}{25}}\)
\(=\frac18\cdot8-10\cdot\frac25=1-4=-3\)
g: \(\frac37\cdot1,5+\frac{\sqrt9}{7}\cdot\frac56-\frac{3}{\sqrt{49}}\cdot\frac{28}{3}\)
\(=\frac37\left(\frac32+\frac56-\frac{28}{3}\right)\)
\(=\frac37\left(\frac96+\frac56-\frac{56}{6}\right)=\frac37\cdot\frac{-42}{6}=-3\)
h: \(\frac{3^{10}\cdot15^5}{25^3\cdot9^7}=\frac{3^{10}\cdot3^5\cdot5^5}{5^6\cdot3^{14}}=\frac35\)
