Question
Simplify the following expression completely: \( \left(-4 w^{6}\right)^{3} \) Answer: Question Help: Video
Ask by Sullivan Fitzgerald. in the United States
Mar 07,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( -64w^{18} \).
Solution
Calculate or simplify the expression \( (-4*w^6)^3 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(-4w^{6}\right)^{3}\)
- step1: Determine the sign:
\(-\left(4w^{6}\right)^{3}\)
- step2: Use the properties of exponents:
\(-4^{3}\left(w^{6}\right)^{3}\)
- step3: Evaluate the power:
\(-64w^{18}\)
The simplified form of the expression \( \left(-4 w^{6}\right)^{3} \) is \( -64w^{18} \).
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Simplify this solution Beyond the Answer
To simplify the expression \( \left(-4 w^{6}\right)^{3} \), raise both the coefficient and the variable to the power of 3. The coefficient \(-4\) becomes \((-4)^3 = -64\), and \(w^6\) raised to the 3 gives \(w^{6 \cdot 3} = w^{18}\). Therefore, the expression simplifies to \(-64 w^{18}\). So, the simplified expression is: \(-64 w^{18}\)
