To find the values of #p(-6)# and #p(1/6)#, we just need to plug those values into the function #6a^3-20a-10# for #a#.
Let’s plug in #-6# for #p# first:
#p(a)=6a^3-20a-10#
#\implies p(-6)=6(-6)^3-20(-6)-10#
#\implies p(-6)=6(-216)-(-120)-10#
#\implies p(-6)=-1296+120-10#
#\implies p(-6)=-1176-10#
#\implies p(-6)=-1186#
Now we do the same for #p=\frac{1}{6}#:
#p(a)=6a^3-20a-10#
#\implies p(\frac{1}{6})=6(\frac{1}{6})^3-20(\frac{1}{6})-10#
#\implies p(\frac{1}{6})=6(\frac{1}{216})-\frac{10}{3}-10#
#\implies p(\frac{1}{6})=\frac{1}{36}-\frac{10}{3}-10#
#\implies p(\frac{1}{6})=\frac{2}{72}-\frac{240}{72}-\frac{720}{72}#
#\implies p(\frac{1}{6})=-\frac{958}{72}#
That can also be expressed as #-13\frac{11}{33}#