Question

what is the answer to (3z)^2(6z^2)^-3? i got 1/54z^4, but my textbook answer key says 1/24z^4. please help!

Answer 1

what am i doing wrong here?

Answer 2

\[(3z)^2(6z^2)^{-3} = (9z^2)(6^{-3}z^{-6}) = \frac{9}{216z^4} = \frac{1}{24z^4}\]

You didn't raise \(6^{-3}\) but instead left it as \(6\)...

Also, \[54z^{-4} = \frac{54}{z^4}\]not \[\frac{1}{54z^4}\]as you wrote.