Simplification of Exponential Expression

Question

How is "(2x^-3y⁶z^-8)(2x)^-6" simplified to "y⁶/32x⁹z⁸"? I understand all of the problem except why it is 32x⁹. I got 128x⁹ instead.

Answer 1

Expand and simplify, using rules of exponentiation.

 

(2x^-3y⁶z^-8)(2x)^-6 = (2 x^-3 y⁶ z^-8)(2^-6 x^-6) = 2^1-6 x^-3-6 y⁶ z^-8 = 2^-5 x^-9 y⁶ z^-8

 

= 32^-1 y⁶ / (x⁹ z⁸) = y⁶ / (32 x⁹ z⁸)