a: \(\left(\frac12\right)^3+\left(5^2\right)^3\cdot\left(\frac15\right)^2+\frac14\cdot4^2-2\cdot3^2-1\)
\(=\frac18+5^6\cdot\frac{1}{5^2}+4-2\cdot9-1\)
\(=\frac18+5^4+3-18=\frac18+625-15=\frac18+610=610,125\)
b: \(\left\lbrack\left(\frac12\right)^3:4\right\rbrack:\frac23+\left(\frac14\right)^2\cdot8-7+18\cdot\left(\frac13\right)^2\)
\(=\frac{1}{32}\cdot\frac32+\frac{1}{16}\cdot8-7+18\cdot\frac19\)
\(=\frac{3}{64}+\frac12-7+2=\frac{3}{64}+\frac{32}{64}-5=\frac{35}{64}-\frac{320}{64}=-\frac{285}{64}\)
c: \(\frac{25^3\cdot5^5}{6\cdot5^{10}}=\frac{5^6\cdot5^5}{5^{10}\cdot6}=\frac{5^{11}}{5^{10}\cdot6}=\frac56\)
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