( – frac{1}{3} w^{-3} z^{-1} )^{-2} = ( – frac{1}{3} )^{-2} square z^{6} square
A) frac{1}{9}
B) frac{1}{9} z^{6}
C) frac{1}{9} z^{-6}
D) frac{1}{9} z^{5}
( – frac{1}{3} w^{-3} z^{-1} )^{-2} = ( – frac{1}{3} )^{-2} square z^{6} square
![[Deleted User]](https://quizzma.com/wp-content/plugins/WPQA/images/default-image.png "[Deleted User]"){kind=avatar}
Share
Quizzma Latest Questions
To solve the equation ((- frac{1}{3} w^{-3} z^{-1})^{-2} = (- frac{1}{3})^{-2} z^{6}), we can start by applying the exponent to each term inside the parentheses.
1. Apply the exponent to each part of the left side:
[
(- frac{1}{3})^{-2} cdot (w^{-3})^{-2} cdot (z^{-1})^{-2}
]
2. Calculate each part:
– ((- frac{1}{3})^{-2} = frac{1}{(-frac{1}{3})^2} = frac{1}{frac{1}{9}} = 9)
– ((w^{-3})^{-2} = w^{6})
– ((z^{-1})^{-2} = z^{2})
Combining these results gives us:
[
9 w^{6} z^{2}
]
3. Set the left side equal to the right side:
[
9 w^{6} z^{2} = frac{1}{9} z^{6}
]
4. Rearranging gives:
– On the right side, (frac{1}{9} z^{6} = 9 w^{6} z