Question

How do you simplify `( 3c^ -4 d^5)^2 * 12cd^ -4`?

Answer 1

`= color(blue)(108 c^(-7) d ^(6)`

Explanation:

`(3c^-4d^5)^color(blue)(2)⋅12cd^-4`

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

Applying the above to the first term:
`= (3^color(blue)(2) * c^color(blue)(-4*2) * d ^color(blue)(5*2))⋅12cd^-4`

`= 9c^color(blue)(-8) d ^color(blue)(10 )⋅12cd^-4`

• As per property:
  `color(blue)(a^m*a^n=a^(m+n)`
  Applying the same to exponents of `c` and `d`

`= (9 * 12 ) * c^(-8) * c^1* d ^10 *d^-4`

`= 108 * c^(-8+1) * d ^(10-4)`

`= color(blue)(108 c^(-7) d ^(6)`