how does 3(-3) to the power n-1 become -1(-3) to the power n

Question

 none really

 

Answer 1

3·(-3)^n-1

= 3·(-3)ⁿ(-3)^-1       [Exponent Property: a^b·a^c = a^b+c]

= 3·(-3)ⁿ·(-1/3)      [Exponent Property: a^-1 = 1/a]

= (-3/3)·(-3)ⁿ

= -(-3)ⁿ

Answer 2

3(-3)^n-1 =3[(-1)(3)]^n-1 = (-1)^n-1•3ⁿ

 

and it also can be simplified in other ways.  If n is odd, the overall result is positive, otherwise negative.