Question

simplify.
\\((-9wu^{2})^{2}\\)
write your answer without parent

Explanation:

Step1: Apply the power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((-9wu^{2})^{2}\), we can apply this rule to each factor inside the parentheses.
\((-9wu^{2})^{2}=(-9)^{2}\cdot w^{2}\cdot (u^{2})^{2}\)

Step2: Simplify each term

• Simplify \((-9)^{2}\): \((-9)^{2}=(-9)\times(-9) = 81\)
• Simplify \((u^{2})^{2}\) using the power of a power rule \((a^{m})^{n}=a^{mn}\). Here, \(a = u\), \(m = 2\), \(n = 2\), so \((u^{2})^{2}=u^{2\times2}=u^{4}\)
• The term \(w^{2}\) remains as it is.

Combining these results, we get \(81w^{2}u^{4}\)

Answer:

\(81w^{2}u^{4}\)