Question

fully simplify.
$(-3x^4y^2)^2$
answer

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, for \((-3x^{4}y^{2})^{2}\), we can apply this rule to each factor: \((-3)^{2}(x^{4})^{2}(y^{2})^{2}\).

Step2: Simplify each factor

• Simplify \((-3)^{2}\): \((-3)^{2}=(-3)\times(-3) = 9\).
• Simplify \((x^{4})^{2}\) using the power of a power rule \((a^m)^n=a^{mn}\): \((x^{4})^{2}=x^{4\times2}=x^{8}\).
• Simplify \((y^{2})^{2}\) using the power of a power rule: \((y^{2})^{2}=y^{2\times2}=y^{4}\).

Step3: Multiply the simplified factors

Multiply the results from Step 2: \(9\times x^{8}\times y^{4}=9x^{8}y^{4}\).

Answer:

\(9x^{8}y^{4}\)