Given expression:
[tex]=(-6x^8)\text{ }\times(9x^{-2})[/tex]The first step in simplification is to open the bracket:
[tex]=\text{ -6 }\times x^8\text{ }\times\text{ 9 }\times x^{-2}[/tex]Next, we collect like terms:
[tex]=\text{ -6 }\times\text{ 9 }\times x^8\text{ }\times x^{-2}[/tex]Applying the laws of indices and multiplying the terms:
[tex]\begin{gathered} =\text{ -54 }\times x^{8-2} \\ =-54x^6 \end{gathered}[/tex]Answer:
[tex]=-54x^6[/tex]