3 c^3 ( 5 c + 2 c^ )

Eme, something is missing in the expression you wrote above. In any case, let's assume that we had

3c^{3}(5c+2c^{q}) where q is any integer (or even just any real number as a matter of fact). Then you would have

3c^{3}*5c + 3c^{3}*2c^{q} where we used the distributive property of multiplication with respect to addition.

Now each term in the addition is a monomial and all you have to do is multiplying the numeric coefficient and compute the exponents of the letteral, c, by applying the rule c^{n}*c^{m}=c^{n+m}. Thus we find

15c^{3+1} +6c^{3+q} = 15c^{4}+6c^{3+q}.

To solve your given assignment, just replace q with the proper value given in the text of your problem and that you forgot to include in the expression at the top.