8. Use the product rule to simplify the $$ \left(m^{6} n\right)\left(m^{15} n^{4}\right) $$

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1. Start with the expression:
   $$
   \left(m^{6} n\right)\left(m^{15} n^{4}\right)
   $$

2. Use the product rule which states that when multiplying powers with the same base, add the exponents. Apply the rule to $$ m $$ terms and $$ n $$ terms separately.

3. For the $$ m $$ terms:
   $$
   m^6 \cdot m^{15} = m^{6+15} = m^{21}
   $$

4. For the $$ n $$ terms (noting that $$ n = n^1 $$):
   $$
   n^1 \cdot n^{4} = n^{1+4} = n^{5}
   $$

5. Combine the simplified $$ m $$ and $$ n $$ terms:
   $$
   m^{21} n^{5}
   $$

The simplified result is:
$$
m^{21} n^{5}
$$
The simplified expression is $$ m^{21} n^{5} $$.

8. Use the product rule to simplify the \[ \left(m^{6} n\right)\left(m^{15} n^{4}\right) \]

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