Answer:
[tex]x^6x^{-12}[/tex] and [tex](x^{-3})^2[/tex]
Explanation:
Given
[tex](x^3x^{-6})^2[/tex]
Required
Possible Next Step
Open Bracket;
From law of indices; [tex](a^m)^n = a^{mn}[/tex]
This implies that
[tex](x^3x^{-6})^2 = (x^{3*2}x^{-6*2})[/tex]
[tex](x^3x^{-6})^2 = x^{6}x^{-12}[/tex]
Hence, a possible next step is [tex]x^6x^{-12}[/tex]
Another possible step is as follows
[tex](x^3x^{-6})^2[/tex]
From law of indices; [tex]a^m*a^n = a^{m+n}[/tex]
This implies that
[tex](x^3x^{-6})^2 = (x^{3+(-6)})^2[/tex]
[tex](x^3x^{-6})^2 = (x^{3-6})^2[/tex]
[tex](x^3x^{-6})^2 = (x^{-3})^2[/tex]
Hence, a possible next step is [tex](x^{-3})^2[/tex]