Lets start by copying the polynomial:
[tex](3x^8)^{15}+(m^{12})^6[/tex]To simplify, we will need to use the following properties:
[tex]\begin{gathered} \mleft(a^cb^d\mright)^f=a^{cf}b^{df} \\ \mleft(a^b\mright)^c=a^{bc} \end{gathered}[/tex]We will apply the first property to the first term and the second property to the second term:
[tex]\begin{gathered} (3x^8)^{15}+(m^{12})^6= \\ =3^{1\cdot15}x^{8\cdot15}+m^{12\cdot6}= \\ =3^{15}x^{120}+m^{72} \end{gathered}[/tex]So, the simplification is:
[tex](3x^8)^{15}+(m^{12})^6=3^{15}x^{120}+m^{72}[/tex]