Question

simplify.
$(-2w^2u)^4$
write your answer without parentheses.

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 \((-2w^{2}u)^{4}\) as follows:
\((-2w^{2}u)^{4}=(-2)^{4}\cdot(w^{2})^{4}\cdot(u)^{4}\)

Step2: Calculate each term

• Calculate \((-2)^{4}\): \((-2)^{4}=(-2)\times(-2)\times(-2)\times(-2) = 16\)
• Calculate \((w^{2})^{4}\) using the power of a power rule \((a^{m})^{n}=a^{mn}\): \((w^{2})^{4}=w^{2\times4}=w^{8}\)
• Calculate \(u^{4}\): \(u^{4}\) remains as it is.

Step3: Multiply the results together

Multiply the three results: \(16\times w^{8}\times u^{4}=16w^{8}u^{4}\)

Answer:

\(16w^{8}u^{4}\)