If two terms have the same base (the letter or number below the exponent), then their multiplication is equal to the number with the same base but with the exponent given by the sum of both exponents. So, in this case we have
[tex]\begin{gathered} r^5k\cdot r^{10^{}}k^{12}=r^{5+10}k^{1+12}=r^{15}k^{13} \\ (\text{if procedure is needed)} \end{gathered}[/tex]So, the condensed expression is
[tex]\begin{gathered} r^{15}k^{13} \\ (\text{ correct answer)} \end{gathered}[/tex]