Apply Laws of Exponents to write an equivalent expression for the given expression. ( – \frac{1}{3} w^{-4} z^{-2} )^{-3} = ( – \frac{1}{3} )^{-3} z^{12} Simplify your answers

To simplify the expression ((- frac{1}{3} w^{-4} z^{-2})^{-3}), we apply the laws of exponents.

1. Reciprocal and Power of a Power: When we raise a product to a negative exponent, we can take the reciprocal of the base and change the sign of the exponent:

[

(a cdot b)^{-n} = frac{1}{(a cdot b)^{n}}

]

Therefore:

[

( – frac{1}{3} w^{-4} z^{-2} )^{-3} = frac{1}{(- frac{1}{3} w^{-4} z^{-2})^{3}}

]

2. Distributing the Exponent: Now apply the exponent to each factor inside the parentheses:

[

= frac{1}{(-frac{1}{3})^{3} (w^{-4})^{3} (z^{-2})^{3}}

]

3. Calculating Each Factor:

– ((- frac{1}{3})^{3} = -frac{1}{27})

– ((w^{-4})^{3} = w^{-12}) (which can be written as frac{1}{w^{12}}))

– ((z^{-2})^{3} =