Thread: Simplification problem

Simplify:

-( (a^2) / (b^3) )^3 (-a^2 b^2)^3

= -( a^6 / b^9) (-a^6 b^6)

= -a^6 * -a^6 * b^(6-9)

= a^12 * b^-3

Did I simplify this correctly? The difficult part is the -(a^6) and (-a^6).

Thanks.

Originally Posted by shenton

Simplify:

-( (a^2) / (b^3) )^3 (-a^2 b^2)^3

= -( a^6 / b^9) (-a^6 b^6)

= -a^6 * -a^6 * b^(6-9)

= a^12 * b^-3

Did I simplify this correctly? The difficult part is the -(a^6) and (-a^6).

Thanks.

The two expressions -(a^6) and (-a^6) are the same. The ones you need to worry about are -(a^6) and (-a)^6.

Since the red negative sign doesn't show up in any parenthesis it is simply a constant factor out in front of everything. For the black negative sign think of it this way:
(-a^2 b^2)^3 = (-1)^3 * (a^2)^3 * (b^2)^3 = -(a^2)^3 * (b^2)^3

which is again outside of everything. So you got it right.

-Dan

Thanks, topsquark for the help and advise.