Question

How do you simplify `(4p^2)^8 / (4p^2)^6`?

Answer 1

`= 16 p^ (4)`

Explanation:

`((4p^2)^8) / ((4p^2)^6)`

• By property:
  `color(blue)((a^m))^n = a ^(mn)`

`((4p^2)^8) / ((4p^2)^6)= ((4^8p^(2 * 8 ) )) / ((4^ 6 p^( 2 * 6))`

`= ((4^8p^ 16 )) / ((4^ 6 p^12)`

`= (4^8 / 4 ^6) * (( p^ 16 )) / ((p^12)`

• By property:
  `color(blue)(a^m / a ^n = a ^(m-n)`

`= 4^((8 - 6 ) * ( p^ (16 -12 ))`

`= 4^(2 ) p^ (4)`

`= 16 p^ (4)`