We will break down the terms and combine like terms before simplifying
[tex]\begin{gathered} \mleft(6m^4n^3\mright)(7mn^5)\text{ = (6 }\times m^4\times n^3\text{ )}\times\text{ (7}\times\text{ m}\times n^5) \\ \text{= 6 }\times m^4\times n^3\text{ }\times\text{ 7}\times\text{ m}\times n^5 \end{gathered}[/tex]collect like terms:
[tex]\begin{gathered} \text{6 }\times m^4\times n^3\text{ }\times\text{ 7}\times\text{ m}\times n^5 \\ =\text{ 6 }\times\text{ 7}\times m^4\times\text{ m}\times n^3\times n^5 \\ =\text{ 6 }\times\text{ 7}\times m^4\times m^1\times n^3\times n^5 \\ \\ \text{when the exponents have same base, the exponents are brought together} \\ \text{If multiplication betw}een\text{ the terms, the exponents are added} \\ \text{if division betwe}en\text{ the terms, the exponents are substracted} \\ \\ =\text{ 6 }\times\text{ 7}\times m^{4+1}\times n^{3+5} \end{gathered}[/tex][tex]\begin{gathered} \text{simplify:} \\ =\text{ 42}\times m^{4+1}\times n^{3+5} \\ =\text{ 42}\times m^5\times n^8 \\ \\ =42m^5n^8 \end{gathered}[/tex]
