Question
8. Use the product rule to simplify the \[ \left(m^{6} n\right)\left(m^{15} n^{4}\right) \]
Ask by Ross Donnelly. in the United States
Mar 15,2025
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Answer
The simplified expression is \( m^{21} n^{5} \).
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To simplify the expression \(\left(m^{6} n\right)\left(m^{15} n^{4}\right)\) using the product rule, you can combine the like bases by adding their exponents. For the \(m\) terms, you add \(6\) and \(15\) to get \(m^{6+15} = m^{21}\). For the \(n\) terms, you add \(1\) and \(4\) to get \(n^{1+4} = n^{5}\). So, putting it all together, you have: \[ \left(m^{6} n\right)\left(m^{15} n^{4}\right) = m^{21} n^{5}. \]