Question

simplify.
$\left(-5wv^{4}\
ight)^{3}$
write your answer without parenthes

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, we can apply this to \((-5wv^4)^3\) as follows:
\((-5wv^4)^3 = (-5)^3 \cdot w^3 \cdot (v^4)^3\)

Step2: Calculate \((-5)^3\)

\((-5)^3 = -5 \times -5 \times -5 = -125\)

Step3: Simplify \((v^4)^3\) using power of a power rule

The power of a power rule states that \((a^m)^n = a^{m \times n}\). So, for \((v^4)^3\), we have:
\((v^4)^3 = v^{4 \times 3} = v^{12}\)

Step4: Combine all the simplified terms

Putting it all together, we have:
\((-5)^3 \cdot w^3 \cdot (v^4)^3 = -125 \cdot w^3 \cdot v^{12} = -125w^3v^{12}\)

Answer:

\(-125w^3v^{12}\)