exponential expression needed simplified

Question

(12x^-3y^-2z³)^-2

(_________)

( 3xy^-2z^-3  )

Answer 1

(12)^-2 (x^-3)^-2 (y^-2)^-2 (z³)^-2

----------------------------------

(3) (x) (y^-2)  (z^-3 )

 

 

Multiply exponents for the top...

12^-2 * x⁶  * y⁴  * z^-6

-------------------------

3xy^-2z^-3

 

Move all the negatives to the other side (top to bottom and bottom to top) and make them positive.

 

x⁶*y⁴*y²*z³  (last two came from the bottom to the top)

----------------

3x(12²)(z⁶)    (last two came from the top to the bottom)

 

 

x⁶ y⁶ z³

-----------

(3*144)xz⁶

 

144

 x 3

-----

 432

 

 

Combine:

 

x⁶y⁶z³

---------   

432xz⁶

 

 

Simplified:

 

x⁵y⁶

------

432z³