Question
Simplify. \( \left(-2 v u^{3}\right)^{5} \) Write your answer without parentheses. D.
Ask by Dunn Summers. in the United States
Jan 30,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(-32\, v^{5}\, u^{15}\)
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The Deep Dive
To simplify the expression \( \left(-2 v u^{3}\right)^{5} \), we raise each factor inside the parentheses to the power of 5. This gives us: \[ (-2)^{5} \cdot v^{5} \cdot (u^{3})^{5} \] Calculating each part: \[ (-2)^{5} = -32, \quad v^{5} = v^{5}, \quad (u^{3})^{5} = u^{15} \] Putting it all together, we have: \[ -32 v^{5} u^{15} \] So the simplified expression without parentheses is: \[ \boxed{-32 v^{5} u^{15}} \]