I have homework on multipling monomials and I need help on how to find the pattern to simplify process.

When multiplying monomials you need to first determine if they have the same base(s). For example, if you have x^{2} ^{* }x^{4} you can just
**keep the base** (*because they have the same base*) and **
add** **the exponents** together to get x^{6}. This is because x^{2} really means x*x and x^{4} really means x*x*x*x. When these two are multiplied together you end up with x*x*x*x*x*x which is equal to x^{6}.

When there are coefficients (numbers in front of the variable) involved you can just
**multiply the coefficients** and then consider the bases as explained above. For example, 5y^{3}(7y^{3}). You can multiply the coefficients (the 5 and the 7) to get 35 and then multiply monomials with like bases (y^{3}
and y^{3}) to get y^{6 }. The overall answer should be 35y^{6}.^{
}

For the more complicated situation there could be more than one variable. In this case
**you can only combine like bases**. For example: 4mn^{5}(10m^{2}n^{3}). Multiply the coefficients first to get 40. Combine the "m" terms to get m^{3} (m=m^{1} so the exponent of 1 needs to be added to
the exponent of 2 to get m^{3}). Combine the "n" terms to get n^{8}. The overall answer should be 40m^{3}n^{8}.

Hope this helps!