Question

How come (-x^3)^n is equal to [(-1)^n][x^3n]?

thanks

Answer 1

Do you know your power laws?\[(ab)^n=a^nb^n\]In this instance you have a=-1 and b=x^3. Then,\[(-1 \times x^3)^n=(-1)^n \times (x^3)^n\]But there's another law:\[(a^n)^m=a^{nm}\]So (x^3)^n becomes\[x^{3n}\]Hence,\[(-x^3)^n=(-1)^nx^{3n}\]