Apply Laws of Exponents to write an equivalent expression for the given expression.
( – 1/6 w^ -2 z^ -4 )^ -1 = ( – 1/6 )^ -1 z^ 2
(Simplify your answers.)
Apply Laws of Exponents to write an equivalent expression for the given expression. ( – 1/6 w^ -2 z^ -4 )^ -1 = ( – 1/6 )^ -1 z^ 2 (Simplify your answers)
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To simplify the expression ((- frac{1}{6} w^{-2} z^{-4})^{-1}), we can apply the laws of exponents. Here’s how to do it step by step:
1. Apply the negative exponent rule: This rule states that (a^{-n} = frac{1}{a^n}). Therefore, we apply this to the entire expression:
[
(- frac{1}{6} w^{-2} z^{-4})^{-1} = frac{1}{- frac{1}{6} w^{-2} z^{-4}}
]
2. Flip the fraction: Inverting the fraction gives us:
[
-6 w^{2} z^{4}
]
Here, (w^{-2}) becomes (w^{2}) and (z^{-4}) becomes (z^{4}).
So, the simplified equivalent expression is:
[
-6 w^{2} z^{4}
]
These steps help us to understand how the laws of exponents work in manipulating expressions with negative exponents. If you have any more questions or need further clarification, feel free to ask!