Question
Use the appropriate property to clear the parentheses. \[ (-4 x y z)^{3}=\square \]
Ask by Cervantes Fleming. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
(-4 x y z)^{3} = -64 x^{3} y^{3} z^{3}
\]
Solution
To clear the parentheses in the expression \[ (-4 x y z)^{3} \], you can use the **Power of a Product Property**. This property states that when a product is raised to an exponent, each factor inside the product is raised to that exponent individually:
\[
(a \cdot b \cdot c)^n = a^n \cdot b^n \cdot c^n
\]
Applying this to your expression:
\[
(-4 x y z)^{3} = (-4)^{3} \cdot x^{3} \cdot y^{3} \cdot z^{3}
\]
Simplifying further:
\[
(-4)^{3} = -64
\]
So, the final expanded form is:
\[
-64 \, x^{3} \, y^{3} \, z^{3}
\]
**Answer:**
\[
(-4 x y z)^{3} = (-4)^{3}\, x^{3}\, y^{3}\, z^{3} = -64\, x^{3} y^{3} z^{3}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To clear the parentheses, we apply the property of exponents that states \((a \cdot b)^{n} = a^{n} \cdot b^{n}\). So, for the expression \((-4xy z)^{3}\), we can break this down as \((-4)^{3} \cdot (x)^{3} \cdot (y)^{3} \cdot (z)^{3}\). Calculating \((-4)^{3}\) gives us \(-64\). Thus, we can rewrite the expression as: \[ (-4 x y z)^{3} = -64 x^{3} y^{3} z^{3} \]
