Divide. Assume that no denominator equals zero. $$ \left(3 m^{5}+m^{6}-m^{8}\right) \div m^{3} $$

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We start with the expression  
$$
\left(3 m^{5}+m^{6}-m^{8}\right) \div m^{3}.
$$

Dividing each term by $$m^3$$ gives:
  
- For the first term:  
  $$
  \frac{3 m^5}{m^3} = 3 m^{5-3} = 3 m^{2}.
  $$
  
- For the second term:  
  $$
  \frac{m^6}{m^3} = m^{6-3} = m^{3}.
  $$
  
- For the third term:  
  $$
  \frac{- m^8}{m^3} = - m^{8-3} = - m^{5}.
  $$

Thus, the divided expression simplifies to:
  
$$
3 m^2 + m^3 - m^5.
$$
The simplified expression is $$3m^2 + m^3 - m^5$$.

Divide. Assume that no denominator equals zero. \( \left(3 m^{5}+m^{6}-m^{8}\right) \div m^{3} \)

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