Упростите выражение при допустимых значениях переменных: а) \(b^{k+5}:(-b)^3\); б) \(-c^n:c^{n-2}\); в) \((-x)^{2m}:x^{m+1}\cdot x^2\); г) \(\dfrac{a^m\cdot a^3}{a\cdot a^{m-1}\cdot a^2}\); д) \(\dfrac{x^9\cdot x^3\cdot x^{2k}}{x^k\cdot x^4\cdot x^8}\); е) \(\dfrac{y^{n+1}\cdot y^{2n}\cdot y^5}{y^n\cdot y^3\cdot y^2}\); ж) \(\dfrac{68x^4y^2z^3}{17x^2y^3z^4}\); з) \(\dfrac{15a^{32}b^{15}c^{56}}{10a^{35}b^{14}c^{56}}\); и) \(\dfrac{80m^{48}n^{22}k^{50}}{16k^{48}m^{45}n^{21}}\); к) \(\dfrac{28p^3q^2-32p^3q^2}{12p^3q}\); л) \(\dfrac{35x^2y^3+55x^2y^3}{15y^3x^2}\); м) \(\dfrac{16ab^2+26ab^2}{32a^2b-11a^2b}\).

1. \(b^{k+5}: (-b)^3=-b^{k+2}\), \(b
   e0\).
2. \(-c^n:c^{n-2}=-c^2\), \(c
   e0\).
3. \((-x)^{2m}:x^{m+1}\cdot x^2=x^{2m-m-1+2}=x^{m+1}\), \(x
   e0\).
4. \(\dfrac{a^{m+3}}{a^{m+2}}=a\), \(a
   e0\).
5. \(\dfrac{x^{2k+12}}{x^{k+12}}=x^k\), \(x
   e0\).
6. \(\dfrac{y^{3n+6}}{y^{n+5}}=y^{2n+1}\), \(y
   e0\).
7. \(\dfrac{68}{17}\cdot\dfrac{x^4}{x^2}\cdot\dfrac{y^2}{y^3}\cdot\dfrac{z^3}{z^4}=\dfrac{4x^2}{yz}\), \(xyz
   e0\).
8. \(\dfrac{15}{10}\cdot a^{-3}b c^0=\dfrac{3b}{2a^3}\), \(a
   e0\), \(b
   e0\), \(c
   e0\).
9. \(\dfrac{80}{16}\cdot m^3n k^2=5m^3nk^2\), \(m
   e0\), \(n
   e0\), \(k
   e0\).
10. \(\dfrac{28p^3q^2-32p^3q^2}{12p^3q}=\dfrac{-4p^3q^2}{12p^3q}=-\dfrac{pq}{3}\), \(pq
    e0\).
11. \(\dfrac{35x^2y^3+55x^2y^3}{15y^3x^2}=\dfrac{90x^2y^3}{15x^2y^3}=6\), \(xy
    e0\).
12. \(\dfrac{16ab^2+26ab^2}{32a^2b-11a^2b}=\dfrac{42ab^2}{21a^2b}=\dfrac{2b}{a}\), \(a
    e0\), \(b
    e0\).

Ответ: а) \(-b^{k+2}\); б) \(-c^2\); в) \(x^{m+1}\); г) \(a\); д) \(x^k\); е) \(y^{2n+1}\); ж) \(\dfrac{4x^2}{yz}\); з) \(\dfrac{3b}{2a^3}\); и) \(5m^3nk^2\); к) \(-\dfrac{pq}{3}\); л) \(6\); м) \(\dfrac{2b}{a}\).